{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vehicle steering\n",
    "Karl J. Astrom and Richard M. Murray\n",
    "23 Jul 2019\n",
    "\n",
    "This notebook contains the computations for the vehicle steering running example in *Feedback Systems*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import control as ct\n",
    "import control.optimal as opt\n",
    "ct.use_fbs_defaults()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle steering dynamics (Example 3.11)\n",
    "\n",
    "The vehicle dynamics are given by a simple bicycle model.  We take the state of the system as $(x, y, \\theta)$ where $(x, y)$ is the position of the reference point of the vehicle in the plane and $\\theta$ is the angle of the vehicle with respect to horizontal.  The vehicle input is given by $(v, \\delta)$ where $v$ is the forward velocity of the vehicle and $\\delta$ is the angle of the steering wheel.  We take as parameters the wheelbase $b$ and the offset $a$ between the rear wheels and the reference point. The model includes saturation of the vehicle steering angle (`maxsteer`).\n",
    "\n",
    "* System state: `x`, `y`, `theta`\n",
    "* System input: `v`, `delta`  \n",
    "* System output: `x`, `y`  \n",
    "* System parameters: `wheelbase`, `refoffset`, `maxsteer` \n",
    "\n",
    "Assuming no slipping of the wheels, the motion of the vehicle is given by a rotation around a point O that depends on the steering angle $\\delta$.  To compute the angle $\\alpha$ of the velocity of the reference point with respect to the axis of the vehicle, we let the distance from the center of rotation O to the contact point of the rear wheel be $r_\\text{r}$ and it the follows from Figure 3.17 in FBS that $b = r_\\text{r} \\tan \\delta$ and $a = r_\\text{r} \\tan \\alpha$, which implies that $\\tan \\alpha = (a/b) \\tan \\delta$.\n",
    "\n",
    "Reasonable limits for the steering angle depend on the speed.  The physical limit is given in our model as 0.5 radians (about 30 degrees).  However, this limit is rarely possible when the car is driving since it would cause the tires to slide on the pavement.  We us a limit of 0.1 radians (about 6 degrees) at 10 m/s ($\\approx$ 35 kph) and 0.05 radians (about 3 degrees) at 30 m/s ($\\approx$ 110 kph).  Note that a steering angle of 0.05 rad  gives a cross acceleration of $(v^2/b) \\tan \\delta \\approx (100/3) 0.05 = 1.7$ $\\text{m/s}^2$ at 10 m/s and 15 $\\text{m/s}^2$ at 30 m/s ($\\approx$ 1.5 times the force of gravity)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vehicle_update(t, x, u, params):\n",
    "    # Get the parameters for the model\n",
    "    a = params.get('refoffset', 1.5)        # offset to vehicle reference point\n",
    "    b = params.get('wheelbase', 3.)         # vehicle wheelbase\n",
    "    maxsteer = params.get('maxsteer', 0.5)  # max steering angle (rad)\n",
    "\n",
    "    # Saturate the steering input\n",
    "    delta = np.clip(u[1], -maxsteer, maxsteer)\n",
    "    alpha = np.arctan2(a * np.tan(delta), b)\n",
    "\n",
    "    # Return the derivative of the state\n",
    "    return np.array([\n",
    "        u[0] * np.cos(x[2] + alpha),    # xdot = cos(theta + alpha) v\n",
    "        u[0] * np.sin(x[2] + alpha),    # ydot = sin(theta + alpha) v\n",
    "        (u[0] / b) * np.tan(delta)      # thdot = v/l tan(phi)\n",
    "    ])\n",
    "\n",
    "def vehicle_output(t, x, u, params):\n",
    "    return x[0:2]\n",
    "\n",
    "# Default vehicle parameters (including nominal velocity)\n",
    "vehicle_params={'refoffset': 1.5, 'wheelbase': 3, 'velocity': 15, \n",
    "                'maxsteer': 0.5}\n",
    "\n",
    "# Define the vehicle steering dynamics as an input/output system\n",
    "vehicle = ct.NonlinearIOSystem(\n",
    "    vehicle_update, vehicle_output, states=3, name='vehicle',\n",
    "    inputs=('v', 'delta'), outputs=('x', 'y'), params=vehicle_params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle driving on a curvy road (Figure 8.6a)\n",
    "\n",
    "To illustrate the dynamics of the system, we create an input that correspond to driving down a curvy road.  This trajectory will be used in future simulations as a reference trajectory for estimation and control."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x324 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# System parameters\n",
    "wheelbase = vehicle_params['wheelbase']\n",
    "v0 = vehicle_params['velocity']\n",
    "\n",
    "# Control inputs\n",
    "T_curvy = np.linspace(0, 7, 500)\n",
    "v_curvy = v0*np.ones(T_curvy.shape) \n",
    "delta_curvy = 0.1*np.sin(T_curvy)*np.cos(4*T_curvy) + 0.0025*np.sin(T_curvy*np.pi/7)\n",
    "u_curvy = [v_curvy, delta_curvy]\n",
    "X0_curvy = [0, 0.8, 0]\n",
    "\n",
    "# Simulate the system + estimator\n",
    "t_curvy, y_curvy, x_curvy = ct.input_output_response(\n",
    "    vehicle, T_curvy, u_curvy, X0_curvy, params=vehicle_params, return_x=True)\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the resulting trajectory (and some road boundaries)\n",
    "plt.subplot(1, 4, 2)\n",
    "plt.plot(y_curvy[1], y_curvy[0])\n",
    "plt.plot(y_curvy[1] - 9/np.cos(x_curvy[2]), y_curvy[0], 'k-', linewidth=1)\n",
    "plt.plot(y_curvy[1] - 3/np.cos(x_curvy[2]), y_curvy[0], 'k--', linewidth=1)\n",
    "plt.plot(y_curvy[1] + 3/np.cos(x_curvy[2]), y_curvy[0], 'k-', linewidth=1)\n",
    "\n",
    "plt.xlabel('y [m]')\n",
    "plt.ylabel('x [m]');\n",
    "plt.axis('Equal')\n",
    "\n",
    "# Plot the lateral position\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(t_curvy, y_curvy[1])\n",
    "plt.ylabel('Lateral position $y$ [m]')\n",
    "\n",
    "# Plot the steering angle\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(t_curvy, delta_curvy)\n",
    "plt.ylabel('Steering angle $\\\\delta$ [rad]')\n",
    "plt.xlabel('Time t [sec]')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linearization of lateral steering dynamics (Example 6.13)\n",
    "\n",
    "We are interested in the motion of the vehicle about a straight-line path ($\\theta = \\theta_0$) with constant velocity $v_0 \\neq 0$. To find the relevant equilibrium point, we first set $\\dot\\theta = 0$ and we see that we must have $\\delta = 0$, corresponding to the steering wheel being straight. The motion in the xy plane is by definition not at equilibrium and so we focus on lateral deviation of the vehicle from a straight line. For simplicity, we let $\\theta_\\text{e} = 0$, which corresponds to driving along the $x$ axis. We can then focus on the equations of motion in the $y$ and $\\theta$ directions with input $u = \\delta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linearized system dynamics:\n",
      "\n",
      "A = [[0. 1.]\n",
      "     [0. 0.]]\n",
      "\n",
      "B = [[0.5]\n",
      "     [1. ]]\n",
      "\n",
      "C = [[1. 0.]]\n",
      "\n",
      "D = [[0.]]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Define the lateral dynamics as a subset of the full vehicle steering dynamics\n",
    "lateral = ct.NonlinearIOSystem(\n",
    "    lambda t, x, u, params: vehicle_update(\n",
    "        t, [0., x[0], x[1]], [params.get('velocity', 1), u[0]], params)[1:],\n",
    "    lambda t, x, u, params: vehicle_output(\n",
    "        t, [0., x[0], x[1]], [params.get('velocity', 1), u[0]], params)[1:],\n",
    "    states=2, name='lateral', inputs=('phi'), outputs=('y')\n",
    ")\n",
    "\n",
    "# Compute the linearization at velocity v0 = 15 m/sec\n",
    "lateral_linearized = ct.linearize(lateral, [0, 0], [0], params=vehicle_params)\n",
    "\n",
    "# Normalize dynamics using state [x1/b, x2] and timescale v0 t / b\n",
    "b = vehicle_params['wheelbase']\n",
    "v0 = vehicle_params['velocity']\n",
    "lateral_transformed = ct.similarity_transform(\n",
    "    lateral_linearized, [[1/b, 0], [0, 1]], timescale=v0/b)\n",
    "\n",
    "# Set the output to be the normalized state x1/b\n",
    "lateral_normalized = lateral_transformed * (1/b)\n",
    "print(\"Linearized system dynamics:\\n\")\n",
    "print(lateral_normalized)\n",
    "\n",
    "# Save the system matrices for later use\n",
    "A = lateral_normalized.A\n",
    "B = lateral_normalized.B\n",
    "C = lateral_normalized.C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue placement controller design (Example 7.4)\n",
    "\n",
    "We want to design a controller that stabilizes the dynamics of the vehicle and tracks a given reference value $r$ of the lateral position of the vehicle.  We use feedback to design the dynamics of the system to have the characteristic polynomial\n",
    "$p(s) = s^2 + 2 \\zeta_\\text{c} \\omega_\\text{c} + \\omega_\\text{c}^2$.\n",
    "\n",
    "To find reasonable values of $\\omega_\\text{c}$ we observe that the initial response of the steering angle to a unit step change in the steering command is $\\omega_\\text{c}^2 r$, where $r$ is the commanded lateral transition. Recall that the model is normalized so that the length unit is the wheelbase $b$ and the time unit is the time $b/v_0$ to travel one wheelbase. A typical car has a wheelbase of about 3 m and, assuming a speed of 30 m/s, a normalized time unit corresponds to 0.1 s. To determine a reasonable steering angle when making a gentle lane change, we assume that the turning radius is $R$ = 600 m. For a wheelbase of 3 m this corresponds to a steering angle $\\delta \\approx 3/600 = 0.005$ rad and a lateral acceleration of $v^2/R$ = 302/600 = 1.5 m/s$^2$. Assuming that a lane change corresponds to a translation of one wheelbase we find $\\omega_\\text{c} = \\sqrt{0.005}$ = 0.07 rad/s.\n",
    "\n",
    "The unit step responses for the closed loop system for different values of the design parameters are shown below. The effect of $\\omega_c$ is shown on the left, which shows that the response speed increases with increasing $\\omega_\\text{c}$. All responses have overshoot less than 5% (15 cm), as indicated by the dashed lines. The settling times range from 30 to 60 normalized time units, which corresponds to about 3–6 s, and are limited by the acceptable lateral acceleration of the vehicle. The effect of $\\zeta_\\text{c}$ is shown on the right. The response speed and the overshoot increase with decreasing damping. Using these plots, we conclude that a reasonable design choice is $\\omega_\\text{c} = 0.07$ and $\\zeta_\\text{c} = 0.7$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAE8CAYAAABQLQCwAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAACOdUlEQVR4nOzdd3zU9f3A8dfnVvZeQAZ7rzAVEQXFhQNX3VpHxVlrl9X6q1U7tK1tbatF0bZu3AgqoKioyB6GkbBDIAMyyR63Pr8/vgckkEDGXS7JvZ99XO/u+/18v9/3JeTt576fpbTWCCGEEEKIwGHydwBCCCGEEKJzSQVQCCGEECLASAVQCCGEECLASAVQCCGEECLASAVQCCGEECLAWPwdQGeIj4/X/fr183cYQgg/2rhxY4nWOsHfcXQWyXtCCGg59wVEBbBfv35s2LDB32EIIfxIKbXf3zF0Jsl7QghoOfdJE7AQQgghRICRCqAQQgghRICRCqAQQgghRIAJiD6AbTF9+vQTtl1zzTXce++91NbWMmvWrBP233rrrdx6662UlJRw9dVXn7D/nnvu4dprryU3N5ebb775hP0///nPufTSS9m5cyd33XXXCfsf+fUj9B7Xm4++/YiXfvcSdrcdp9uJW7tRKIbfNJzB4wbj2Otg3f/WEWwOJtgSTKglFKUUzz77LOnp6XzxxRf8/ve/P+H8L/7rWYYmR/Hxoo/469xXATdoDShQitf//hip/QfzzuJvmfvaO6DMTY5///33iY+P55VXXuGVV1454fyLFy8mNDSUf//737z77rsn7F/y+ZfYXW6e/dtf+XzpYgCUUiggNDSEpUuWoJTid7/7HV9++WWTY+Pi4vjggw+Mn9Mjj7B69eom+1NSUnjjjTcAePDBB8nIyGiyf8iQIcybNw+AOXPmsGvXrib709PTefbZZwG46aabyMvLa7J/ypQpPPXUUwBcddVVlJaWNtl/7rnn8pvf/AaAiy66iLq6uib7L7nkEn7xi18AXfPf3v/93/8xc+ZMMjIyePDBB0/Y/8c//pEzzjiDVatW8etf//qE/af8t/fiiwwdOpSPP/6Yv/71ryfsf/3110lNTeWdd95h7ty5TfZ9/fXXJ5QXgcvudLNyTwmbDhwms6CS/MN11DlcOFxuokNtJEQEMSA+jDEpUYxPi6FffJi/QxbCr6QC2IU53A6Ka4t55LtHcBx0ULe/jhpHDUHmIMIsYZhMJrTWpEWkobUmuyKbgzUHObK+s1KKEEsIL2x+gQvCLqCqugpcdqivgIYqsNeAow5ePBPizbDTAYX2EwN571aIMsE2B+y3gzKB2QYWG5iD4Js/Q9pQKNxpnM8SDErhcLmps7t4e/0Biutg6YZcth+sxOHSOF1uXFrjcmuGP7YUgIq1u6nbf7jJpZUliAG/XkyI1UzFyr3U5JZjNiksnsfBegt/XrqD2DAbOw9VUV7rwGpWWM0mrGa5wS1ET7e/tIaXV+zj4y0FlNc6MCkYlBhOv7gwQm1mLGYT5bV2iqoaeGd9Ga+sygFgQHwY5w5PZHZ6MiP7RKKU8u8HEaKTqSOVhZ5s4sSJujuNhnO4Hbye9TovbH6BOmcdU3pP4fJBlzOp1yQSQk8+i4XD5SC3Opfdh3ezo2wHWaVZbC3eQpWjGoAIl5sxDQ2MdbgYG5bKqNjhRMYNgog+EBoLwVFGpc5kBu0GtxMctVBfaVQca0uhphiqC6GyACrzoSIf3I6jMbgxUUA8+1yJ7NdJ5Ohe5NGLmvA0nFF9CQ+PIDbURkSwhbAgC8FWMzaLCYtJoZRx89GtNU6Xxu5yU+9wUWt3UWt3Ut3gorreQWW9k4o6B+W1dsprHTjdzf87jgqxkhARREJ4EAkRQSRGBJEYGURiRPDR9wkRQUSFWOU/AD2cUmqj1nqiv+PoLN0t77VVea2df365h9fX5GBSivNH9uKKcX04Y2A8wVZzs8e43Jo9RdWsyS7li+2FrMkuxeHSDOsVwfWT07h6QgphQXJfRPQsLeW+Tq8AKqX+C1wCFGmtRzWzXwH/AGYBtcCtWutNnn0XevaZgZe11k+35prdKRHuq9jHz77+GXvK9zAjdQa/mPgL0iLT2n4irWHft7DyH7j3fkWO1cKW3sPJiE5ks65lb3U+GuN33z+qP6PiRjEibgQj4kYwJGYI4bbwU14iu7iazzIL+XrHQfIO7KOPLqK/uYj08HKGB5WSoguIrs/Hai9vemBEH4jtDzH9jEd0X4hOMx4RvYzKZ5s+qqaqwUlZtZ3SmgZKqu2UVDdQUmWnuLqekio7RVX1lFQbz/UO9wnnsJlNJEQEEd+ospgQbiM+Ioj4cOMRF24jPiyIyBCLVBa7IakA9hxrs0v58fzvKalu4JqJqfzsvCEkRga3+TwVtQ4Wbc7n3Q15bM2vICLYwvWT07jjzP4kteN8QnRFXakCeBZQDbzWQgVwFvBjjArgacA/tNanKaXMwC7gPCAPWA9cr7XOOtU1u0siXH9oPQ8ufxCLycLjUx5nRtqM9p1o/2r48gk4sBrCe8GEH0L6jRDT92iRKnsVW0u2sq1kG1uLt5JZmklxXfHR/cnhyQyMHsjAqIH0j+pPakQqqRGpKHckH31fwMKMAjILKgEY0TuS6UMTmDIwjvFpMSd+g64tg8P7oGwflGUfey7fD1UHm5Y1WSCyD0SmeJ57Q0Rvo2IYngRhiRAWDyEx0I5K2JHKYnFVA0WVDRRXN1BUWU9xlfG6uOrYo6zWTnN/HhaTIibMRmyojZgwK7FhNqJDbcSEWokOsREVaiUq5NgjIthCRLCViCALJpNUHP1FKoDdn9aaF77J5pnPd5IWG8q/rh/HqOQor5x704HD/G9lDou3HsSsFFdPTOHe6QNJiQn1yvmF8JcuUwH0BNMP+KSFCuCLwNda6/me9zuB6UA/4HGt9QWe7Y8AaK2fOtX1ukMiXLZ/GQ99+xCpEan8+9x/kxKR0vaT1JTCsscg4w3jLtu0n8G4m8Haum+yRbVFbC/dzq7Du9h1eBd7K/aSU5GDo1Hzrnab0c5oQs2x9I3qzcikZFKjEokJiiEqKIoIWwThtnDCLGGEWcMIsgQRYg7BYmrhrpmjDiry4PB+o0JYmQ/luZ7m5TyoPAiuhhOPM1kgJNZotg6JRQdH4Q6Oxh0cgTsoArctHLct1HhYQnBbg3BbgtHmILQlCLfJgrZY0SYr2mRBm8y4lRlMJjSgMfopltfZOVxjp7zOTlmN0dxcXmenos5BRa2DijoHlfUOquqcVDY4cJ94c7GJUJvZeARZCLGaCLFaCLEdeW3CZlGEWk0EmUwEWxU2iyLIjPFsMvZbTWA1GRVRiwKrmWP9IhWYTGBGYTEZw/yV0pg92xVwrFarOaGGe7J80Ow+7+cPjUYbkaK1xmjd10cvrzVH714PHXgOytS6vp5SAezetNY8+UkW/1uZw8VjevP0laOJCLZ6/ToHSmt54du9vL8hD43m2kmp3DdjEL2jQrx+LSE6Q0u5ryt2dkgGchu9z/Nsa277aZ0Yl89sKtzEw98+zKi4UTx37nNEBbXjG+3uL2DBHKOf3pk/hbN+Cba2jXJLDE0kMTSRs1PPPrrt212F/P3rtWwpzCY09DDDUpzER9dQ5z5Mcd0+luxfT52z7iRnPcZmsmE1WzErMxaTBZMyYeJIrQTUkf/ooyEM3GGxuHtFg3bjdrtwaSfa7calXWg0Lu1GU4tL16IdeeAAqtr0kTsuxPOIMZ5ao87zaMLheYg22TwgA7mn2vO53ZrHFm3jjTUHuOPM/vzfxcN91g0jLS6UP14xmh+fM4jnl+/hnfW5vLshj1tO78s90wcSFx7kk+sK0dm6YgWwub9qfZLtzZ9EqTnAHIC0tHb0oesk+yv388DyB+gT3od/nfOvtlf+XE5Y/gf47m+QOBJ++AkkjehwXJtzy/nzZztYuaeU3lFhPDL9Mq6bnEZ4Mx2k65x1lNeXU2mvpNJeSZW9ilpnLbWOWuqd9dS76rG77NjddhwuB27tNqaxwY1bG7fMtD5y38f4NZuU6ejzkddmZT763qzMKKWafTZphXI7MLudKNexZ5PbicntQrkcKO1CuZyYtBvldoF2YdIa5XahtBu0C4UGt0bhRnnuQik06Mb/GBv902zyHyRlPJTntVLHyplMR1/rI/uO7FcKDbhRuDW43OBC4XJrXEY4uLSx78jDhWe8DuDy3NRzaeOn6dYce/ZM7eP2RH3kjprb8zE0R/6gjJE4upk/Od3oMzb3B3lsd9NyJ/63WnH0J6Ka7lfHPzc6wfE/YREYnl66gzfWHOCuswfw8IXDOqUPbu+oEH5/+WjuOmsg//xyN/9duY/56w5w51kD+NG0Ac3mQiG6k674LzgPSG30PgUoAGwtbG+W1noeMA+MphDvh9lxtY5a7v/yfkyY+Pe5/yY6OLptJ7DXwvu3w64lMP6HcNGfwNqxZorS6gb+tHQH727IIzbMxmOXjODG09MIsrQ8MCPEEkJIeAi96d2hawshxPHe35jHvG+zufn0vp1W+WssNTaUv/xgLHedPYBnPtvFs1/s5rXV+7lvxiBuPC2txRHHQnR1ba4AegZx/B6IAzYDz2qt13kxpkXA/UqptzGaeCu01geVUsXAYKVUfyAfuA64wYvX7XT/2PQPcipz+M/5/yE1MvXUBzRWUwrzr4W8DTDrGZh8Z4di0Vrz4aZ8nvwki5oGJ3POGsCPzxnkkz42QvQknZATA9bG/WX8+sOtnDEwjscuHeHX0feDEiN44eYJbM4t5y+f7eR3n2Tx8opsHjh3MFdPSJF5R0W30547gP8F7gEygAnAs0qpZ7XWJy7x0Ayl1HyMQR3xSqk84LeAFUBr/QKwGGME8B6MaWBu8+xzKqXuBz7DmAbmv1rrzHbE3yWsP7Set3a8xY3Db2Ry78ltO7i2DF69BEr3wrWvw/BLOxRLcVUDv16wlWVZhUzqF8MfrxjN4KSIDp1TiADSoZwomldea+eeNzbROzqY528Y32UqWGNTo3njR6exak8Jf/l8J498uJV/f72HB84ZzBXjkrF0kTiFOJU2jwJWSq3RWp/e6H04sKa5Eb1dRVtGw3XGclxu7WZbyTaUUoyMG8kvf/HL1i/H9cCPoXCr0fybNAKCozu0HFdlnQP76Xdgj+jNBeF5bFn65gl9q062HBd0fCm4I0t6PfPMM3zyySdN9oWEhLBkyRIAWQpOloJrsq+tS8H5ahRwV82JbR0F3NX+/e0uqkaPvYLPn7kfZ/E+3/z7++dfGZoax8cLF/LXF17lWE9YBcrE68/9idT+A3nnk6+Y+9/XTzj+vffeY1up5qe/f5Yd335MkNVMclQI8RE2TEpJ7pPc16VzX6vvACqlXgM2Ad8ppR4D/qi1dgINQH2boglwB2sO0uBqYFjssKMDHFrF0QBFWcYSbgnDoa19Bo+Tf7iOvMO1pIdYefXHZ7Jz3ddsXdqhUwoRMCQn+k5ptZ3S6gZ+NC6ZUclRZBSf+piTctRDXTnYq42How6c9TDv7GPLYB5qZhnMN644tgxmjh3MVs/DBmYbasVfmZE2hJ+MsvOvLAt5VW6yS6rJO2yiV1QwFXUOQmUaQdFFtfoOoFLqbCAdGOt5jsVopu0PvKm1fsw3IXZcV5oPq6SuhFkfzuKslLN45uxnWn+g1rDwPsh4E676D4w+8RtPa9XZXfz8vQwWbz3E5el9+MMVo2X5I9HjefsOYFfPiV0p77VFUVU95//9W/rGhfHB3VPa36RaXQRZC41H7lpjHXQwVhxKHGE8R6VAaLyxBKYtFExWY61zt9NY3tJea1QY68qhrgxqSozzVh+CqkPGRPa66eSfjqAYct0JZNXHUGRKJCF1COPHjCG53zCITm3z9FxCdFSH7wBqrb8Bvml0QjMwAiP5jfVGkIHgxc0v4nA5+PG4H7ftwDVzjcrf2Q93qPJXVFnPj17bwNb8Ch6dNZwfTesvy5oJ0Q7eyokdWR6zJ/rz0p3UNDj56w/Gtr3ypzXsXwmrn4ddS43KWcJwmDwHBkyHlEkQEu29YF1OozJYkWdMYF9xAGv5AQaUHyC5JAdz5SYseR8bc1scCTEkDhWdalQ+o1IgMtmz6lGfY6sedXA2ByFaoy1NwFMw+rUYM6Jp7QK2eh5v+Ca8niW3Mpf3d73PlYOvpG9k31MfcET2N/D5ozDsEjj7V+2+/oHSWm76z1qKqxp48aYJnD+yV7vPJUSg82JOfAV4Dnithf0XAYM9j9OAufSQSfCP9/2Bw7y/MY+7zx7IoMRTr0feRPbX8MXjUPC9sUrQ1J/A6Gu8Mi9qi8yWYxW5tNOb7AoCcLs5XJzH8jUbyMzaRlB1Hv10CaNMVaTV7CAs+2uUvfrE8wZHNV36MizeuFMZGudZ/Sja6AIUHA3BkRAUCZagdi2P2R1orT1zoWrcbnBrjVvrZicCNqYNVZiUMduoUmBSCrPJs62H/ozaoy3tfj8EnldK7QKWAku11od8E1bPNHfzXKxmK3ePvbv1B9WUwodzIG4wXPGiZxLhttt5qIqb/7OWBqebt+48jXFpMe06jxDiKK/kRK31t57lMVsyG2PtdA2sUUpFK6V6a60PnuSYbsft1jy+KJPEiCDuP2dQ6w8sy4Ylv4Ldn0NUKlzydxh7fde4i2YyEZOUxpWz07jisitYn3OYjzLyeWrrQQ7XOgixmjl/YDDnp7iZFFdPImWepuVDUFNkNDcXbjOanuvLW7yMBpwmC/agcBps4dhtoTiswcbDbMNhseEwW3CaLDhMZpwmCy5lwmlSxrNSuJUJF+BSxkT0LuWpaKFwo3GD59nz8HQfO/Jao3FqN06XG4fLjcPlwuFy43K7cbiNZ5dbG8/ajftIhU670e5j59Bao5ssEHDkE2JMxO95rzgyXEc3+Uk0naS/mQnj1bFjGk9Sr5rsP7aj0RT+zU9Y3+hA1XjHceVo5thjF2vhmBYMi0rngWueO0WpU2tLE/DdAEqpYRjfSF9RSkUByzGS30rPN2DRjMKaQpbsW8L1w68nITShdQdpDYt+bPQ9ufE9CGrjN2KPHYcquX7eGmwWE+/dPYUhMsWLEB3WiTmxpeUxT6gAdpcVkJrz/qY8NudV8Pdrx7ZulQ23G9a/DF/81lgb/LwnYfJdrV77vLMppZjcP5bJ/WN54rKRrN5bymeZBXyxax8fZ5ehzHXERTrpm2CjV0wKUYl9CE6149B11DhqqLXXUGuvpNZeTb3Ts8qS2069y0GDduJuUhGq5+g4JI3Pl5pU2qh4Hbk9ocBYWYljlZmj6x+ZMFZWMhkVsSYVrMbnbPa1p1LWeAEm3bSMblRUNXeLsBVrCLVp2bGTnKPZY7ywLEVI5b6On4R2zAOotd4B7AD+rpQKAWYAPwD+BgTMQutt9fbOt3Hj5oZhbZi7euMrsPNTOP8P0HtMu667u7CKG19aS5DFzDt3nU7fOOmALIQ3dUJObPV/j7rDCkjNaXC6eHbZLtJTo7k8PfnUB9SWwQd3wN6vYNBMuPSfENWK4zpRpb2S/Kp8DtYc5GDNQQprCymqLaKktoTS+lJK6kqoaKhA99Icycp1wA4X7CgBSkC7bJgIxmYKJdgcQqg1lHBbHNEhqUTawgi3hRBmCybcFkKoNZggcxA2sw2b2YbVZMWirChlAW3G5Tbhcpqod4Ddqaiza2obNNUNmuo6J9W1Tqrq7FTVOqiodVBdZ6fO7sakPU2p+shCnYpgi4WYMBuxoUFEh9qIDg0iOsRKVKiNyBAbUSEWIkOCCA+2EhFiIyLYSniIlSCLBVBgMtNkiUxlarQkpugs7VkJ5Avg51rrzVrrOoyJmxd7PbIepM5Zx3u73uOc1HNIiUhp3UEVefDZo9D/bDj93nZdN6ekhutfWovZpHjrztOk8ieED3RCTmxpecwe4+11uRRU1PPnq8eeuo/WoW3w9g3GCNxL/g4TbvNbxcHhdrC/Yj97K/aSXZ5NTmUO+yv3c6DqAFX2qiZlrSYriaGJxIfE0y+yHxOSJhATHENMUAwxwTFEBUURFRRFpC2S2norB4rd7DxUw56iavaV1nKgtIa82pPfxjN5+ruBZz1w3brbf8FWE7GhNmLDw4kJtdEvIYjYMBtx4Tbiw4OICzOeYz3PITZZ/q4naM/cHw9hfNPdD/y6p/VD8YWP935MRUMFN484cTLKZmkNi39pjGC77J/t6vdXXNXALf9dh8vt5u27pzAgoX3Nx0KIU/J1Tmx2eUwvX8Nv6h0unl++h8n9Y5k6KO7khfcuh7dvNAY+3LYEUjqv0cnpdrLr8C62lWwjszST7aXb2VO+B4fbqFwpFH3C+9A3si+z4meRGpFKn/A+9AnrQ1JYEnHBca0fgBABQxPgvOPGr9TZXRysqKOsxk5ZjZ2KOge1dhc1dicOp8bhcqOP9m9TWM0mrBZFiNVMsNVMWJCF8CAz4UFWokKMR3SoVdYzDlDtaQLeBJyjlLoKWKqU+hD4s+ebrziO1po3tr/BiLgRjEsc17qDdnwCOxcbfVpi+rX5mtUNTm57ZR3FVQ28dedpDEqUPn9C+EpHc2J7l8f0Nn+txlAYPZL8nL04P36NGfObrj3eZDWGOTdD8Q6whkJSP/j4Fz5djUGjeeTvj5BjyuHdd95lw4INuDxdOi0mC6HWUO756z2M6z+ObUu2seS9JdSrenZ6/geyCpKsBNI1VgJpSbtm//XMS7UTYzqC3wN3KqUe0VqfuFZOgNtYuJF9Ffv4/dTft+7bX0MVLH4Ikka1q+nX5db8+K1NbD9Yxcu3TJTRvkJ0go7kRK319afYr4H7vBJoF2N3unjhm72M7xtN1W5rywX3fgVFO4yBcEkjjUEfPuB0OylvKKeioYIKewU/Wf4TguKCCHGEEB8ST7gtnDBrGEHmIADuTb+X+Ph4SsNL27aqkxBdQHvWAv4OGABkAmuAtRgdoH8CBGmt53g7yI7y54z4v131W5buW8rya5YTam3FmkBfPAHf/Q3u+AJSJ7X5en9cvJ1532bz+8tHcdPpbZhrUIgezodrAXfJnNgdVgJ5a+0Bfr1gK/PvPJ0pA1to/t27HN78ASRPgJvehyDvtmhUNFTwWc5nfJ7zOesL1+PWbhJDE5mWPI0z+pzB5F6Tie7gsptC+FOHVwJp5G4gU59Yc/yxUmp7u6Lroeqd9XyW8xnn9T2vdZW/8lxY829j8tJ2VP7e35jHvG+zuWVKX6n8CdF5JCe2g9uteXlFNmNSojh9QGzzhQq+h3dugvjBcMPbXqv8ubWbVQWr+GDXB3yT9w0Ot4N+kf24Y9QdzOw7k+Gxw2XCYNHjtacP4LaT7L64A7H0OF8d+IoaRw2XDbysdQd8+aTxfG7blxDdmlfBrxds5YyBcfzmEh/OfC+EaEJyYvt8uaOI7JIa/nX9uOYrW5UF8OY1xqoeN30IIR3vzlJlr+KDXR/w9s63ya/OJzY4luuGXcelAy5lWOwwqfSJgOLVjhRa62xvnq+7W5S9iN5hvZnYqxWtTvkbYeu7cObPjAXD26Ci1sE9b24kPszGczeMx9rexdOFEF4lObFlL32bTXJ0CBeNamZJSmcDvHsL2Gvgh4sgsneHrlVSV8Krma/y3q73qHHUMDFpIg+Of5Bz087Faj5J30MhejDf9KQVFNUWsbpgNXeMuqN1nYO/fNJY6/HMn7bpOm635mfvZlBYWc87d00hNszWzoiFEKJzZOSWsy6njMcuGYGluS+sSx+GvPXwg1cgcXi7r3O4/jD/2fof3tn5Dna3nQv6XcCtI29lRJy0kgjRnomgg4CrgH6Nj9daP+m9sLq/JfuW4Nbu1jX/7l9tLGR+/h+M+a3a4L8r9/HljiIev3QE42XErxCdTnJi2722OofwIAvXTGqmtWPr+7DhvzD1JzDyinadv8HVwFvb3+KlLS9R46zh4v4XM2fMHPpF9etY4EL0IO25A7gQqAA2Ag3tuahS6kLgH4AZeFlr/fRx+38J3NgoxuFAgta6TCmVA1QBLsDpi1F93vDlgS8ZGjO0dQnn6z9CWCJMvL1N18gsqODPS3dy3ogkfnhGK64jhPCFDufEQHK4xs4nWw5y7cTUE9f8rciDT34GKZPgnLb3hQZYmb+SP6z9A7lVuZyVchY/Hf9TBsUM8kLkQvQs7akApmitL2zvBZVSZuB54DyMJY7WK6UWaa2zjpTRWv8F+Iun/KXAT7XWZY1OM0NrXdLeGHytpK6EjKIM7hl7z6kL56yEfd/CBX8EWytGCnvU2V385O0MokOt/OmqMdJ5WQj/6VBODDTvb8zD7nSfOFOB2w0f3QNuJ1w5D8xt+89TWX0ZT619iqU5S+kb2ZcXz3uRM/qc4cXIhehZ2lMBXKWUGq213trOa04G9hzpHO1Z3mg2kNVC+euB+e28ll8sz12ORnNO2jmnLvz1UxCe1Oa7f08t2c6eompev2Oy9PsTwr86mhMDhtuteXPtfib1i2For+OmdFn3ovFl+NJ/QuyANp33qwNf8cTqJ6i0V3Lv2Hu5ffTtRydrFkI0rz0VwDOBW5VS+zCaOxTGZPVjWnl8MpDb6H0exvqWJ1BKhQIXAvc32qyBz5VSGnhRaz2vhWPnAHMA0tLSWhmad3x54EtSwlMYEjPk5AXzNkDOCuPunzWk1edftaeE11bv5/ap/Zk2OKGD0QohOqijOTFgrNxbQk5pLQ/OPC43lufCl7+DwRfA+Ftafb56Zz1/Wv8n3t/1PsNih/HS+S+dOu8KIYD2VQAv6uA1m2urbGk5kkuBlcc1/07VWhcopRKBZUqpHVrrb084oVExnAfGjPgdjLnVquxVrD24lhuH3XjqZtmV/4DgKBj/w1afv6bByUMfbKF/fBi/vGBoB6MVQnhBR3NiwHhr7QFiw2xcNPq4qV+WPARouPgZaGV3lpyKHH7xzS/YeXgnt426jR+n/1imdBGiDdozEfR+pdRYYJpn0wqt9eY2nCIPaDz0KwUoaKHsdRzX/Ku1LvA8FymlFmA0KZ9QAfSXFXkrcLqdnNv33JMXLN0L2z82pn0JCm/1+Z9esoP88jrevWsKITZzB6MVQnSUF3JiQCirsfPF9kJ+OKUfQZZGuWv7J7BzMZz3JES3rrXmu/zveOibhzCbzDx/7vOclXKWj6IWoudq84zBSqmfAG8CiZ7HG0qpH7fhFOuBwUqp/kopG0Ylb1Ez14kCzsYYYXdkW5hSKuLIa+B84GSz8He6Lw98SVxwHGMTxp684OrnwWyF0+5q9bnX55Tx+pr93HZGfyb1a2HpJCFEp/JCTgwICzPycbg0V09MObbRXmPc/UscCaffe8pzaK15I+sN7vvyPvqE9+GdS96Ryp8Q7dSeJuA7gNO01jUASqk/AauBf7XmYK21Uyl1P/AZxjQw/9VaZyql7vbsf8FT9Arg8yPX8UgCFniaVi3AW1rrpe34DD7hcDtYVbCKC/pdcPLJn2tKIONNGHMtRDQzC34zGpwuHvlwK8nRIfziAunjIkQX0qGcGCje35jH6OQohvVqNNfpquegMh+uetn4QnwSbu3mmQ3P8HrW65yTeg5PTXuqdWusCyGa1Z4KoMKYg+8IF83362uR1noxsPi4bS8c9/4V4JXjtmUDp7i15j9bi7dS7ag+9dQDG/8Hzno4o/U3CV78Jps9RdX879ZJhNpkARchupAO58SeLqugksyCSp64bOSxjVWHjH7Qwy+DvifPmQ63g8dWPsYn2Z9ww7Ab+NXkX7VuhSUhRIvaU5P4H7DW0/8O4HLgP16LqBtbVbAKkzJxWu9mBzUbXE7Y8D8YMB0SWjeII7u4mueW7+HiMb2ZMSzRO8EKIbxFcuIpvL8xD5vZxGVj+xzb+NXvwWWH85446bEOl4NffPMLvsr9ih+P+zF3jr5T5j0VwgvaMwjkb0qpb4CpGN9yb9Naf+/1yLqhVQWrGB0/mqigqJYL7VxsNHnM+kurzqm15reLMgkym/jtJbJ+pRBdjeTEk3O43CzMyGfmiERijsxZWpgJ378BU+476Zx/jSt/D09+mBuH39hiWSFE27SrLVFrvRFj2SPhUV5fzraSbade/WPdPIhKhSGtWzjg86xCVuwu4bFLRpAYGeyFSIUQ3iY5sWUrdhdTWmPnynGNBn989QcIioSzftHicU63k19++0u+yv2KRyY/wg3Db+iEaIUIHK3uRKGU+s7zXKWUqmz0qFJKVfouxO5hzcE1aDRnJJ+kL0vRdmPi50l3gOnUU7jUO1z87pMshiZFcMuUvqcsL4ToPJITW2dRRgFRIVbOGuKZtL7ge9j5KZxxP4TENHuM1ponVz/Jlwe+5FeTfiWVPyF8oNV3ALXWZ3qeI05VNhCtLFhJpC2SUXGjWi60/mUwB8G41s10/8I3e8k7XMf8O0/HYpYOz0J0JZITT63O7uLzrEJmpydjs3hy2PI/GhW/0+5u8bh/bPoHC/Ys4K4xd3HTiJs6KVohAkt75gH8U2u2BRKtNavyV3F679Mxt3Rnz14LW96FkZdDWNwpz1lQXscL3+zl4jG9mTLw1OWFEP4hObFlX2wvpNbuOjb4I3c97P4czngAgiObPebdne/yn23/4QdDfsB96fd1YrRCBJb23FY6r5ltAb0U0t7yvRTVFTE1eWrLhbIWQkNlq5d9+8tnO3FreOSiYV6KUgjhI5ITW7BocwG9IoOZ3N8zcf03T0NoPEye02z51QWr+ePaPzIteRqPnvaojPYVwoda3QSslLoHuBcYoJTa0mhXBLDS24F1J+sL1wOcfPqXTa9B7MBTzncFsDm3nAXf53Pv9IGkxMhEp0J0RZITT66i1sHXO4v44ZR+mE0KDm6GPV/AuY81u/xlTkUOP//m5/SP6s+fz/pzy60pQgivaMso4LeAJcBTwMONtldprcu8GlU3s/7QenqH9SY5PLn5AiW74cAqmPnEKRc611rzu0+yiA+3ce+MQT6IVgjhJZITT2Jp5kEcLs3sdE9e/O5ZY+TvpB+dULbWUctPlv8Ei7Lwr3P+Rbit9eujCyHapy2DQCqACuB634XT/Wit2Vi4kal9TtL8u+k1MFlg7Kl/dJ9lHmLD/sP88YrRhAfJih9CdFWSE0/uky0H6RsXyqjkSCjLhqyPjNWPgpvOk6q15sk1T7KvYh/zzp9HSkRK8ycUQnhVR6eBqQr0KQ+yK7Ipqy9jUq9JzRdwOWDzfGPev4ikk57L6XLz56U7GZQYzjUTJQkK0ZVJTmzZ4Ro7q/aWMmt0b6Mf36p/GV+CT7/3hLLv7nyXT7M/5b70+zi99+l+iFaIwCTTwHTQhkMbAJiYNLH5Anu+gJpiGHfqqQze3ZBHdkkN826eINO+CNHFSU5s2bKsQlxuzaxRvaG6GL5/E9JvgIheTcrtLNvJn9b/iTOTz+TOMXf6KVohAlOb2xiVUj8Almqtq5RS/weMB34XqEsfrS9cT1JoUsvNFpvnG6PeBs086Xlq7U6e/WIXE/rGcN6Ik98pFEJ0HZITT/Tp1oOkxoYYzb/f/BlcDTDl/iZl6p31PLziYaKCovjDmX/ApORLr2iew+EgLy+P+vp6f4fSpQUHB5OSkoLVam1V+fZ0MvuN1vo9pdSZwAXAM8ALwEmGwPZMWms2HNrA6X1Ob366grrDsHMpTLwdzCf/hfxvZQ5FVQ08f+N4mfpAHCWJr+3amgS9QHJiI+W1dlbuKeGOM/ujXHZjAvxB50H84Cblnt30LHvK9zB35lxig2P9FK3oDvLy8oiIiKBfv37y38cWaK0pLS0lLy+P/v37t+qY9lQAXZ7ni4G5WuuFSqnH23Gebm9f5T5K60uZlNRC/7/Mj4xvvmOvO+l5KmodvPDNXs4dlsikfpIIxTGS+NqmPUnQCyQnNrIsqxCnWzNrdG/IXAA1RXB60zXSVxWs4s3tb3LDsBs4M/lMP0Uquov6+nrJgaeglCIuLo7i4uJWH9Oee+75SqkXgWuAxUqpoHaep9s72v+vVwv9/za/DQnDoPfYk55n3oq9VNU7+dn5Q7wdoujm6uvriYuLk8TXSkeSYCffMZWc2MjirQdJjg5hTHIkrPk3xA+Fgecc3V/jqOGJVU/QL7IfP53wUz9GKroTyYGn1tafUXuS1DXAZ8CFWutyIBb4ZTvO0+1tKtpEfEg8aRFpJ+4sy4bcNcbdv5P8UkqqG/jfyhwuHtObkX2iWiwnApckvrbxw89LcqJHZb2DlXtKuWhUL1TuWmPy59PuapIDn934LAdrDvLk1CcJtgT7MVohAlubK4Ba61pgL3CBUup+IFFr/XlbzqGUulAptVMptUcp9XAz+6crpSqUUhmex2OtPbYzZRRlMC5xXPP/wdnyHqBg9DUnPcfcr/dS73Dx05ly90+I7sgbObGnWL6jCLvLzYWjesH6l4w5/xp1gdlYuJG3d77NDcNvYFziOD9GKoRocwVQKfUT4E0g0fN4Qyn14zYcbwaex1grcwRwvVJqRDNFV2it0z2PJ9t4rM8V1xaTX53P2IRmmne1hq3vQb8zIaqF1UGAwsp6Xl+znyvHpzAoUWa+F6I76mhO7Ek+zywkPjyI8XFOyFoEY28AWxgADpeDJ1Y/QXJ4Mg+Me8DPkQoh2tMEfAdwmtb6Ma31Y8DpQFsmcJoM7NFaZ2ut7cDbwOxOONarNhdvBiA9Mf3EnYe2QOluGHXVSc8x9+u9uN2aB84ZfNJyQvR0S5cuZejQoQwaNIinn366xXL9+vVj9OjRpKenM3FiC31vO19Hc2KPUO9wsXxnEeeNSMKU8Qa4HcYMCB6vZr3Kvop9PHrao4RaZY1z0f3Mnz+f9PR0Ro8ejVKKceM6fhfbn7mvPRVAxbFRb3het6XTTTKQ2+h9nmfb8aYopTYrpZYopUa28ViUUnOUUhuUUhvaMiqmtTKKMrCZbIyIbeYG5Nb3jVnvR7RcNz1UUc9b6w5w1fgU0uIkGYrA5XK5uO+++1iyZAlZWVnMnz+frKysFssvX76cjIwMNmzY0IlRnlRHc2KP8N3uEmrtLi4YkQAb/wf9pkGC0bWloLqAFze/yLlp5zItZZqfIxWifa6//nree+89IiIiuOOOO/j00087dD5/5772VAD/B6xVSj3umepgDfCfNhzfXGLUx73fBPTVWo8F/gV81IZjjY1az9NaT9RaT0xISGhDeK3zffH3jIofhfX4+f3cbtj2AQw8F0JbntJl7td7cLs1958zyOuxCeFtixYt4uqrr26ybe7cuTzwQMeb8tatW8egQYMYMGAANpuN6667joULF3b4vJ2oozmxR/gs8xARQRamqi1QfqDJ3b+n1z2NUopfTfqVHyMUomMyMzO57LLLeOyxx3j55Zfp06dPh87n79zX5nkAtdZ/U0p9DZyJUSG7rY0z3ucBqY3epwAFx12jstHrxUqpfyul4ltzbGdocDWQVZrFzSNuPnFn7hqozIeZj7d4/KGKeuavy+XqCSmkxsrdP9E6T3ycSVaBd5eYHdEnkt9eOvKU5R599FHmz5/fZNvAgQP54IMPTnrctGnTqKqqOmH7M888w8yZxuo4+fn5pKYe+7NOSUlh7dq1zZ5PKcX555+PUoq77rqLOXPmnDJ2X/NCTkQpdSHwD8AMvKy1fvq4/dOBhcA+z6YPj/SN7gqcLjdfbC/knOGJWDf9BcISYdglAKzMX8ny3OX8ZPxP6B3e28+Riu7OX3nQ4XBwyy23MG/ePKZNO/Vd7O6Q+9ozETRa600Yd+naYz0wWCnVH8gHrgNuaFxAKdULKNRaa6XUZIw7laVA+amO7QxZpVk43U7SE9JP3Ln1fbCEwNBZLR7/wjd7cWvNfTPk7p/o+jZv3ozb7WbUqFHs37+fxYsXc8899+BwOE455cqKFStOeX6tT7yJ39J5V65cSZ8+fSgqKuK8885j2LBhnHXWWa37ID7UkZzYaHDbeRhfctcrpRZprY9vC1qhtb6kY5H6xvqcwxyudXDZAAVLlsLUB8Biw+l28pf1fyElPIVbRtzi7zCFaLelS5cycuTIVlX+oHvkvvasBRwM3IvxbVcD32HMft+qmVe11k7PVAmfYXzb/a/WOlMpdbdn/wvA1cA9SiknUAdcp42fVLPHtvUzdFRGUQbAiSOAXU7IWghDL4Sg5kf1FlUaff+uHJ8sd/9Em7TmTp0vZGRkMGHCBACWLVvG7t27AcjKymLs2LE4nU4eeughlFL07du3SbNwa74Fp6SkkJt7rGtvXl5ei00rR7YnJiZyxRVXsG7dOr9XADuaE2k0uM1zviOD21ruDNTFLMsqxGYxMa1mGWgXjDNaRz7Y9QF7K/by9+l/x2a2+TlK0RP4Kw+uW7eOGTNmNNnW3XNfe+4AvgZUYfTNA7geeB34QWtPoLVeDCw+btsLjV4/BzzX2mM7W0ZRBmkRacSFxDXdsf87qC2BkVe2eOy8b7NxueXun+g+3G431dXVuFwuPvzwQ5KTk6mrq+OVV17h9ddfZ+7cucyePZuzzz77hGNb8y140qRJ7N69m3379pGcnMzbb7/NW2+9dUK5mpoa3G43ERER1NTU8Pnnn/PYY481c8ZO19Gc2NzgtubWEZ6ilNqM0e3lF819+VVKzQHmAKSlNTNBvQ9orfk86xBTB8Ri2/oW9D0T4gZSaa/k+YznmZg0kXPTzu2UWITwlYiICFavXs1tt912dFt3z33tGQQyVGt9h9Z6uecxBwiYWYy11mQUZzQ//1/mArCGweDzmj22pLqBN9buZ3Z6H/rGhfk4UiG8Y9asWWRnZ5Oens7dd99NZmYmEydOZM6cOYwfP55NmzYxderUdp/fYrHw3HPPccEFFzB8+HCuueYaRo489i1/1qxZFBQUUFhYyJlnnsnYsWOZPHkyF198MRdeeKE3PmJHdTQndmRgXNODfDz4rTk7DlWRd7iOG3vnGSsgjTfu/v1n638obyjnl5N+KavZiG7vzjvvpLi4mOHDh3PJJZdQUVHR7XNfe+4Afq+UOl1rvQZAKXUasLLDkXQTBTUFlNWXtdD8u8ho/rWGNHvsyyv20eB0y90/0a0kJSWRkZFx9P1ll13WZP/ll1/OXXfdRWxsLI888gixsS2Pfm/JrFmzmDWr+X6zixcfu+G/efPmNp+7E3Q0J7Z7YJzWuqQDcXvFsqxClIIzKxdDUCQMv4zCmkLe3P4mFw+4mBFxfpmrXwiviomJYcGCBQBcfPHF7Nixo9vnvvZUAE8DblFKHfC8TwO2K6W2AlprPcZr0XVBW0u2AjAqYVTTHTnfQl0ZjLyi2ePKa+28vjqHS8b0YWCCrPoheo7Zs2cze7Zf5mPvKjqaEzsyMM7vPs86xNRkC8G7P4H0G8AWygsb/4JLu7gv/T5/hyeEV7355pvExcUxadIkTCZTt8597akAdok2F3/ZWrwVm8nGkOjjWngyF4AtHAbNbPa4V1blUGN3cd+MgZ0QpRCiE3UoJ3ZwYJxfFZTXsS2/klfHbIOSehh3MzkVOSzYvYBrh15LSkSKv0MUwqtuvPFGbrzxRn+H4RXtmQdwvy8C6S62lWxjeNzwphNAuxyw/WMYelGzzb/VDU7+tzKH80YkMaxXZCdGK4TwNW/kxI4MjPOnL7YXAnBaxVJIGA59xvHct7/EZrZx55iAWw1PiG6lPYNAApbD7SCrNIvR8aOb7tj3LdQdhhGXN3vcG2v2U1Hn4H7p+yeE6EGWZRVydtxhggs3QfoN7Dy8i89yPuPmETcTHxLv7/CEECchFcA22Fu+l3pX/YkVwKyFnubfE6c6qHe4eHnFPqYNjmdsanTnBCqEED5WWe9gTXYpd0WtA2WGMdfwwuYXCLeGy6TPQnQDrW4CVkpV0fy6uwqjo3OPb9vcUrwFoGkF0OWEHZ/AkAuabf59Z30uJdUN3DdjXGeFKYToBIGeE7/eWYzL5WJi+Wcw6Fx2Oir44sAX3D32bqKCovwdnhDiFFpdAdRaR/gykO5gW8k2ooOim3Zs3r8SakthxIkjgexONy9+s5eJfWM4rX/bh4cLIbquQM+Jy7IKuTB0J7baQ5D+NHM3zyXCGsFNw2/yd2hCiFaQJuA22FqylVHxo5pOapq1EKyhMOjEyZ8XZuRTUFHPfTMGyUSoQogew+508/WOIn4UsQaCo9iZMJAvD3zJTSNukrt/QnQT7ZkGBqVUDDAYCD6yTWv9rbeC6opqHDXsLd/L+X3PP7bR7TJG/w4+H2xN1/V1uTVzv97LiN6RTB/aOTPyCyH8I9By4rp9ZbgbqhhbvQLG3cBL218jzBrGjcN7xvQYQgSCNlcAlVI/An6CMVt9BnA6sBo4x6uRdTFZpVloNKPiG00AfWAN1BQ12/y7dNshsktqeP6G8XL3T4geLBBz4rKsQ1xq24DZVU/OoOl8vvY33D7qdrn7J0Q30p4m4J8Ak4D9WusZwDig2KtRdUFHVwBpXAHMWgiWYOMOYCNaa55bvocB8WFcOKpXZ4YpRLe0dOlShg4dyqBBg3j66adP2L9z507S09OPPiIjI3n22Wc7P9DmBVRO1FrzxfYifhi6BmL685+SDdjMNm4aIX3/RM82f/580tPTGT16NEopxo3r+OBOf+a+9lQA67XW9QBKqSCt9Q5gqFei6cIySzJJDk8mJjjG2OB2w/ZFxsofQU2Xdvt6ZzHbD1Zy9/SBmE1y90+Ik3G5XNx3330sWbKErKws5s+fT1ZWVpMyQ4cOJSMjg4yMDDZu3EhoaChXXNH8sot+EFA5MbOgEnd5HsPqMygYeQmfZH/CVYOvknn/RI93/fXX89577xEREcEdd9zBp59+2qHz+Tv3tacCmKeUigY+ApYppRZy3MLlPVFmaSYj40Ye25C/AaoOwvDLmpQ7cvcvOTqEK8Yld3KUQvjGokWLuPrqq5tsmzt3Lg888ECHz71u3ToGDRrEgAEDsNlsXHfddSxcuLDF8l9++SUDBw6kb9++Hb62lwRUTvw8q5ArLCtRaF61OQG4bdRtfo5KCN/LzMzksssu47HHHuPll1+mT58+HTqfv3Nfm/oAKqMz2wNa63LgcaXUciAKWOqVaLqosvoy8qvzuXbotcc2Zi0EkxWGNl0GdO2+MjbuP8wTl43EapZB1sKLljwMh7Z695y9RsNFJzY7HO/RRx9l/vz5TbYNHDiQDz744KTHTZs2jaqqqhO2P/PMM8ycaaybnZ+fT2pq6tF9KSkprF27tsVzvv3221x//fWnjLkzBGJO/HzbQV4KXsXh3pP48MCXzBowi15h0tVFdBI/5UGHw8Ett9zCvHnzmDZt2ilP2R1yX5sqgFprrZT6CJjgef+N1yLpwrJKjVuyR/v/aQ1Zi2DgDAhu2un5+eV7iA+3ce2k1ONPI0S3tHnzZtxuN6NGjWL//v0sXryYe+65B4fDccoBTitWrDjl+bU+cS7lls5rt9tZtGgRTz31VOuC97FAy4kHSmsxF20lNegAc3tPob54NbeNlLt/oudbunQpI0eObFXlD7pH7mvPNDBrlFKTtNbr23tRpdSFwD8AM/Cy1vrp4/bfCPzK87YauEdrvdmzLweoAlyAU2s9sb1xtNa2km0oFMNjhxsbDmZAxQGY/qsm5TbnlrNidwm/unAYwVazr8MSgaYVd+p8ISMjgwkTJgCwbNkydu/eDUBWVhZjx47F6XTy0EMPoZSib9++TZqFW/MtOCUlhdzc3KP78vLyWmxaWbJkCePHjycpKclrn88LOpwTu4vPsw5xpfk7as025ldmcXbK2QyKkTXORSfyUx5ct24dM2bMaLKtu+e+9lQAZwB3eypiNRxb9mhMaw5WSpmB54HzgDxgvVJqkda6cc/HfcDZWuvDSqmLgHnAaY1j0FqXtCP2dsksyaRfVD/CbZ7BHlkLjbUvh85qUu655XuICrFy85Qu0zdJiA5zu91UV1fjcrn48MMPSU5Opq6ujldeeYXXX3+duXPnMnv2bM4+++wTjm3Nt+BJkyaxe/du9u3bR3JyMm+//TZvvfVWs2Xnz5/fZZp/G+lQTuxOvsgs4N/W1SwaMIHDDfncPup2f4ckRKeIiIhg9erV3HbbsTve3T33taeT2kXAAIw5ri4FLvE8t9ZkYI/WOltrbQfeBppMpKe1XqW1Pux5uwZjfi2/ySzNZFTccc2//c+C0GPLu20/WMmyrEJum9qP8KB2za8tRJc0a9YssrOzSU9P5+677yYzM5OJEycyZ84cxo8fz6ZNm5g6dWq7z2+xWHjuuee44IILGD58ONdccw0jRx4bcDVr1iwKCgqora1l2bJlXHnlld74WN7U0ZzYLZRWNxCS+w1RupxXzXWMTRjLuERZ41wEhjvvvJPi4mKGDx/OJZdcQkVFRbfPfe2pqRwAbgQGaK2fVEqlAb2A/a08PhnIbfQ+j6Z39453B7Ck0XsNfK6U0sCLWut5zR2klJoDzAFIS0trZWgnKqwppLiumJHxnl9K4TYo2wtn3N+k3PPL9xAeZOHWM/q1+1pCdEVJSUlkZGQcfX/ZZU1Hvl9++eXcddddxMbG8sgjjxAb2/Z1r2fNmsWsWbOa3bd48eKjr0tLS9t87k7Q0ZzYLXy5vYjLTd+xLCqevIYyfj7yNzLJvQgYMTExLFiwAICLL76YHTt2dPvc154K4L8BN8a33Scx+uN9gDERams0lzFO7AkJKKVmYFQAz2y0earWukAplYgx5cKO5pZc8lQM5wFMnDix2fO3xrbSbQDHpoDJ/AiUCYYd+4K/t7iaT7ce5O6zBxIdamvvpYTolmbPns3s2SeuhhNAOpoTu4WvtuzlWfMG7kwcSmpIJDNSZ5z6ICF6mDfffJO4uDgmTZqEyWTq1rmvPU3Ap2mt7wPqATxNtW2p9eQBjYfIptDMnFlKqTHAy8BsrfXRqq/WusDzXAQswGhS9pnMkkzMysyw2GGe5t+PoN+ZEH5sfd/nvtpDsMXMHWf292UoQoiuqaM5scurqHMQtW8JO4Mgw1nBTcNvwmySgW4i8Nx444289tprmEzdf5q39nwCh2cghwZQSiVgfPttrfXAYKVUf6WUDbgOWNS4gKcJ5UPgZq31rkbbw5RSEUdeA+cD29rxGVotszSTQdGDCLYEQ2EmlO6BEZcf3Z9dXM3CjHxuntKX+PAgX4YihOiaOpoTu7yvdhRyufqW/8X1IsIWweWDLvd3SEKIDmpPBfCfGHfeEpVSfwC+A1o9MY3W2gncD3wGbAfe1VpnKqXuVkrd7Sn2GBAH/FsplaGU2uDZngR8p5TaDKwDPtVa+2zCVa21MQDkyPx/WQuN5t9Gq388t3wPNouJO6cN8FUYQoiurUM5sTtYu2kzqUE7WR6kuGbINYRaQ/0dkhCig9rcB1Br/aZSaiNwLkZ/vsu11tvbeI7FwOLjtr3Q6PWPgB81c1w2MLatMbdXXlUeFQ0VxgCQI82/facebf7NKalhYUYBt53Rj4QIufsnRCDyRk7symoanPTK+Yg3EyIwKRPXD+ty0/AIIdqhzXcAlVJ/0lrv0Fo/r7V+Tmu9XSn1J18E52+ZpZkAxhQwRduhZBeMONbh819f7cFiUsw5W+7+CRGoenpOXL6jkHPN3/JBZBQX9r+IpLAuNQm3EKKd2tMEfF4z2y7qaCBd0baSbdhMNmOm+8wPjeZfTwVwT1EVC77P44dn9CMxItjPkQoh/KhH58TtG5azKbKGOqW5ecTN/g5HCOElrW4CVkrdA9wLDFBKbWm0KwJY5e3AuoJtpdsYFjsMq7LA1veNyZ/DEwH4+xe7CbGauessufsnRCAKhJxY0+Ckz/4PebVvJBMS0hkRN8LfIQkhvKQtfQDfwpiQ+Sng4Ubbq7TWZV6NqgtwuV1klWYZo90KvofD+2DazwDILKjg0y0H+fE5g4iTkb9CBKoenxO/3LqfsPCNHLRE8qtRt/o7HCGEF7W6Aqi1rgAqgOuVUjHAYCAYQClFc5Mxd2c5lTnUOeuMCaC3fQAmKww3Jn/+2+e7iAy28CMZ+StEwAqEnHhozXt8GxVESnA801Om+zscIYQXtWcQyI+AbzGmcXnC8/y4d8Pyv20lxvSCo2JHwLYPYdBMCIlh3b4yvtxRxF1nDyQqxOrnKIXoGZYuXcrQoUMZNGgQTz/9dIvlbr/9dhITExk1alQnRndyPTUnHq6xE1rxIZuDg7hp9B0y8bMIePPnzyc9PZ3Ro0ejlGLcuI6vhe3PnNaeQSA/wVjiaL/WegYwDij2alRdwLaSbYRaQulXWQhVBTD6arTW/GHxdnpFBnP7VFn1QwhvcLlc3HfffSxZsoSsrCzmz59PVlZWs2VvvfVWli712dSf7dUjc+K369bzfXQJYcrKFYO9uwi9EN3R9ddfz3vvvUdERAR33HEHn376aYfP6c+c1p4KYL3Wuh5AKRWktd4BDPVuWP6XWZrJiLgRmLd9CJYQGHIhn249yObccn52/hBCbPJtWASORYsWcfXVVzfZNnfuXB544IEOn3vdunUMGjSIAQMGYLPZuO6661i4cGGzZc8666x2LbjuYz0yJ5Z8/xJfhIVyzaDZMvGzEEBmZiaXXXYZjz32GC+//DJ9+vTp8Dn9mdPaPBE0kKeUigY+ApYppQ4D+d4Myt8cLgc7y3Zy/dBr4Kt/w7CLaTCH8Oel6xnWK4Krxqf4O0QRgP607k/sKNvh1XMOix3Gryb/6pTlHn30UebPn99k28CBA/nggw9Oety0adOoqqo6YfszzzzDzJkzAcjPzyc19djy4CkpKaxdu7Y14XcVPS4nFpRVc8C8GoWNG8be5e9whDjKX3nQ4XBwyy23MG/ePKZNm3bKc7Ym9/lbe1YCucLz8nGl1HIgih7wbbexXYd3YXfbGdVgh/pySL+BV1bmcKCslldvn4zZpPwdohCdZvPmzbjdbkaNGsX+/ftZvHgx99xzDw6HA6VO/rewYsWKU55fa33CtlOdtyvpiTlx5bLX+CzSwvSoUfQK6+XvcITwu6VLlzJy5MhWVf6gdbnP39pzB/AorfU3AEqpA8BfvBJRF7ClxJjSa+z+TRDRh4Nxp/GP175j5vAkzh6S4OfoRKBqzZ06X8jIyGDChAkALFu2jN27dwOQlZXF2LFjcTqdPPTQQyil6Nu3b5Nm4dZ8C05JSSE3N/fovry8PK80rfhDT8iJbrcm6+Cr1MSYuHPqI/4OR4gm/JUH161bx4wZM5ps62ju87cOVQAb6T5f11thS/EWEoLj6LXjG5j6AH9YsguXW/PbS2USVBF43G431dXVuFwuPvzwQ5KTk6mrq+OVV17h9ddfZ+7cucyePZuzzz77hGNb8y140qRJ7N69m3379pGcnMzbb7/NW2+95YuP0pm6bU5ct2kt30ZUMsrUi5GJY/wdjhBdQkREBKtXr+a22247uq2juc/f2jMIpDkntuF0Y1uKtzDaHIHSLjbFXMQnWw5yz/SBpMZKR2gReGbNmkV2djbp6encfffdZGZmMnHiRObMmcP48ePZtGkTU6dObff5LRYLzz33HBdccAHDhw/nmmuuYeTIkU2uX1BQABij8KZMmcLOnTtJSUnhP//5T4c/n49025z41fqnKLJYmDPpQX+HIkSXceedd1JcXMzw4cO55JJLqKio6HDuA//mtLYsBVdF80lNASFei8jPyuvLOVB1gCvtNlzJE/nZV7WkxYZy99kD/R2aEH6RlJRERkbG0feXXXZZk/2XX345d911F7GxsTzyyCPtGtE2a9YsZs2a1ey+xYsXH319/EAUf+qJObH0cBmrLbtIc4Yyfehlpz5AiAARExPDggULALj44ovZsWOHV3KfP3NaW1YCifBlIF3Fkf5/Y0pzWZxwBTmltcy/83SCrTLtixDNmT17NrNnz/Z3GJ2uJ+bEt5c8SY7Nws9TrupWA3GE6CxvvvkmcXFxTJo0CZPJ1K1zn7f6APYYW0u2YgKGum38cPdwbpvajykD4/wdlhBC+JTdbmd59RckmhU3Tv+Fv8MRoku68cYbufHGG/0dhld4qw9gj7Hl4HoG2R0scU2nV3wcD10wzN8hCSGEz73xye/ZGaS4NHYmVrPN3+EIIXzMLxVApdSFSqmdSqk9SqmHm9mvlFL/9OzfopQa39pjO8Kt3Wwt3sKY+npeqj+Xv12bLit+CCF8riM50RvcLhdLij8i3qm55+I/ePPUQoguqtMrgEopM/A8cBEwArheKXX8/CoXAYM9jznA3DYc2245Zbup0g5sdUnMuWIm6anR3jq1EO3W3ETJomXd7efVkZzoLW8v+zs7gjUXhp9BkE1mOxBdT3f7u/aHtv6M/HEHcDKwR2udrbW2A28Dx/einA28pg1rgGilVO9WHttuC78ycmpIryu5ZmLqKUoL4XvBwcGUlpZK8mslrTWlpaUEBwf7O5S26EhO9IqFB94kzunm3ku75dzVooeTPHhq7cl9/hgEkgzkNnqfB5zWijLJrTwWAKXUHIxvyqSlpbUqsH4Jgzhj1wbuue2nrSovhK+lpKSQl5dHcXGxv0PpNoKDg0lJ6VbrdXckJx5sXKg9ec9hb2CIbSCTghOICI1qW+RCdALJg63T1tznjwpgc3MLHF+tb6lMa441Nmo9D5gHMHHixFZ9bbhi+v1cMf3+1hQVolNYrVb69+/v7zCEb3UkJzbd0I68Z7UF8btb329NUSH8QvKgb/ijApgHNG5fTQEKWlnG1opjhRCiO+lIThRCiHbxRx/A9cBgpVR/pZQNuA5YdFyZRcAtnpFvpwMVWuuDrTxWCCG6k47kRCGEaJdOvwOotXYqpe4HPgPMwH+11plKqbs9+18AFgOzgD1ALXDbyY7t7M8ghBDe0pGcKIQQ7aUCYVSNUqoY2N/K4vFAiQ/D6Urks/ZMgfJZ2/o5+2qtE3wVTFfTxrwHgfPvBgLnswbK5wT5rCfTbO4LiApgWyilNmitJ/o7js4gn7VnCpTPGiifs7ME0s8zUD5roHxOkM/aHrIUnBBCCCFEgJEKoBBCCCFEgJEK4Inm+TuATiSftWcKlM8aKJ+zswTSzzNQPmugfE6Qz9pm0gdQCCGEECLAyB1AIYQQQogAIxVAIYQQQogAIxXARpRSFyqldiql9iilHvZ3PL6klMpRSm1VSmUopTb4Ox5vUkr9VylVpJTa1mhbrFJqmVJqt+c5xp8xekMLn/NxpVS+5/eaoZSa5c8YvUUplaqUWq6U2q6UylRK/cSzvcf9Xjub5L2eIVDyHgRO7vN13pMKoIdSygw8D1wEjACuV0qN8G9UPjdDa53eA+dOegW48LhtDwNfaq0HA1963nd3r3Di5wT4u+f3mq61XtzJMfmKE/i51no4cDpwn+fvsyf+XjuN5L0e5RUCI+9B4OQ+n+Y9qQAeMxnYo7XO1lrbgbeB2X6OSbSD1vpboOy4zbOBVz2vXwUu78yYfKGFz9kjaa0Paq03eV5XAduBZHrg77WTSd7rIQIl70Hg5D5f5z2pAB6TDOQ2ep/n2dZTaeBzpdRGpdQcfwfTCZK01gfB+KMCEv0cjy/dr5Ta4mkm6RFNPo0ppfoB44C1BNbv1Rck7/Vsgfb30WNzny/ynlQAj1HNbOvJc+RM1VqPx2j6uU8pdZa/AxJeMRcYCKQDB4G/+jUaL1NKhQMfAA9qrSv9HU8PIHlP9BQ9Nvf5Ku9JBfCYPCC10fsUoMBPsfic1rrA81wELMBoCurJCpVSvQE8z0V+jscntNaFWmuX1toNvEQP+r0qpawYSfBNrfWHns0B8Xv1Icl7PVvA/H301Nzny7wnFcBj1gODlVL9lVI24DpgkZ9j8gmlVJhSKuLIa+B8YNvJj+r2FgE/9Lz+IbDQj7H4zJGk4HEFPeT3qpRSwH+A7VrrvzXaFRC/Vx+SvNezBczfR0/Mfb7Oe7ISSCOeYePPAmbgv1rrP/g3It9QSg3A+PYLYAHe6kmfVSk1H5gOxAOFwG+Bj4B3gTTgAPADrXW37kTcwuecjtEEooEc4K4jfUW6M6XUmcAKYCvg9mz+NUZ/mB71e+1skvd6hkDJexA4uc/XeU8qgEIIIYQQAUaagIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAoxUAIUQQgghAozF3wF0hvj4eN2vXz9/hyGE8KONGzeWaK0T/B1HZ5G8J4SAlnNfQFQA+/Xrx4YNG/wdhhDCj5RS+/0dQ2eSvCeEgJZzX5dqAlZK/VcpVaSU2tbCfqWU+qdSao9SaotSanxnxyiEEN6mlLpQKbXTk9sebmb/dKVUhVIqw/N4zB9xCiF6ji5VAQReAS48yf6LgMGexxxgbifEJIQQPqOUMgPPY+S3EcD1SqkRzRRdobVO9zye7NQghRA9TpeqAGqtvwXKTlJkNvCaNqwBopVSvb11/Up7Jd8Xfe+t0wkhRGtMBvZorbO11nbgbYxc12nWbVvGqowlnXlJIYSfdakKYCskA7mN3ud5tnnFgt0LuGXJLZTXl3vrlEIIcSqtzWtTlFKblVJLlFIjmzuRUmqOUmqDUmpDcXFxqwP47eqf8tLax9sSsxCimzvlIBClVGwrzuPWWpd3PJxTUs1s080WVGoORjMxaWlprTp5/6j+AGRXZDM+WLoXChHIOjH3tSavbQL6aq2rlVKzgI8wusI0PUjrecA8gIkTJzabG5sTTTCVqrbVAQshur/WjAIu8DyaS1JHmIHW1bI6Jg9IbfQ+BSO2E7QnEQ6MHgh4KoBJUgEUIsB1Vu47ZV7TWlc2er1YKfVvpVS81rqkg9cGINYSw3Z3PmXV9cSGB3vjlEKILq41FcDtWutxJyuglOqsjnOLgPuVUm8DpwEVWuuD3jp577DehFhC2Fu+11unFEJ0X52V+9YDg5VS/YF84DrghuOu0wso1FprpdRkjO47pV64NgBJEX1YUX2QrF3bOHP8RG+dVgjRhbWmAjjFS2VOSSk1H5gOxCul8oDfAlYArfULwGJgFrAHqAVu88Z1jzApE/0i+7GvYp83TyuE6J46JfdprZ1KqfuBzzDuKP5Xa52plLrbs/8F4GrgHqWUE6gDrtNat7qJ91QGJg1B12xi7951UgEUIkCcsgKota73RpnW0Fpff4r9GrjPG9dqycDogWwolMlThQh0nZz7FmN8wW287YVGr58DnvPGtZqT1msMZL9NUXGzU7AKIXqg1gwC+dnJ9mut/+a9cPxvQNQAPsn+hBpHDWHWMH+HI4Twk0DKfUlxQwCoqcvxbyBCiE7TmmlgIjyPicA9GNMTJAN3Y0xa2qMMiB4AIM3AQoiAyX29wo3pVN0UU1rd4OdohBCdoTVNwE8AKKU+B8Zrras87x8H3vNpdH4wIMqoAO4t38uo+FF+jkYI4S+BlPsirBEEaxPaUs3W/AqmD030d0hCCB9ry0TQaYC90Xs70M+r0XQBqRGpWEwWsiuy/R2KEKJr6PG5TylFkjWMGoud7blF/g5HCNEJWjMK+IjXgXVKqQUYk5ReAbzmk6j8yGKy0C+yH9nlUgEUQgABkvt6hyRQWF1CZM52QFo/hOjpWl0B1Fr/QSm1BJjm2XSb1rpHLpw7IGoAO8p2+DsMIUQXECi5LykimdWHd5F2cJe/QxFCdIK2rgW8D1gNfA9EKKXO8n5I/jcgegB51Xk0uKQztBACCIDc1ytmECVmM1F1ORRXSe4ToqdrdQVQKfUj4FuMyUqf8Dw/7puw/Gtg1EDc2k1ORY6/QxFC+Fmg5L6kyFTcShFvzWNbfoW/wxFC+Fhb7gD+BJgE7NdazwDGAcU+icrP+kf1B5CBIEIICJDc1yu0FwAR1kK25EkFUIieri0VwPojs94rpYK01juAob4Jy7/6R/XHoizsPrzb36EIIfwvIHJfUlgSAFbbYbbml/s3GCGEz7VlFHCeUioa+AhYppQ6DBT4Iih/s5lt9I/uLwNBhBAQILkvKdSoAFaZHeTk5qL1RJRSfo5KCOErraoAKiMLPKC1LgceV0otB6KApT6Mza+GxQxjzcE1/g5DCOFHgZT7Im2RhJhsHLKYia3JprCygV5Rwf4OSwjhI61qAtZaa4xvv0fef6O1XqS1trd8VPc2LHYYxXXFlNSV+DsUIYSfBFLuU0qRFJpIocXCEFMeW/LK/R2SEMKH2tIHcI1SapLPIulihscNB2Bn2U4/RyKE8LOAyX29IlIotNoYYspnq4wEFqJHa0sFcAawWim1Vym1RSm1VSm1xVeB+duQmCEAbC/b7udIhBB+FjC5Lyk0iUNWG2ODDrJZRgIL0aO1ZRDIRT6LoguKCooiOTxZ7gAKIQIm9/UK60WJctNX57I1rxyttQwEEaKHastScPt9GUhXNDRmqIwEFiLABVLu6xPeBzdQrapQNaXkHa4jNTbU32EJIXzglE3ASqlN3ijTHQ2LG8b+yv3UOmr9HYoQopMFYu5LjUgF4IDFymCVLxNCC9GDteYO4PBT9HdRGNMi9DjDY4ej0ew6vIv0xHR/hyOE6FwBl/uOVADzrBaGW/LZklfOxWN6+zkqIYQvtKYCOKwVZVwdDQRAKXUh8A/ADLystX76uP3TgYUYC7MDfKi1ftIb127OsFjjo28v2y4VQCECT6flvq4iMTQRm8lGbnAok8MKeTW33N8hCSF85JQVwM7q/6KUMgPPA+cBecB6pdQirXXWcUVXaK0v6YyYkkKTiA6KloEgQgSgQOr7d4RJmUiJSOGAM58r6w6yNb8Cl1tjNslAECF6mrZMA+Nrk4E9WutszySrbwOz/RmQUoqhsUPJKj2+DiqEED1TWkQauRYLfew51Npd7Cmq9ndIQggf6EoVwGQgt9H7PM+2401RSm1WSi1RSo1s6WRKqTlKqQ1KqQ3FxcWtiyBjPvx9NDgbjm4aEz+GXYd3yUAQIURASIlIIU83YLOXEUslGbmH/R2SEMIHWjMK+HalVJDn9Wyl1F1KqTN8EEtzbQz6uPebgL5a67HAv2i0RNMJB2o9T2s9UWs9MSEhoXURBIVDxQE4uPnopvTEdFzaRWZpZuvOIYToETox93UpqRGp1GknJWYT6cEHyciVkcBC9EStuQP4E611g1LqceBnQH/gt0qpVUqpXl6MJQ9IbfQ+BShoXEBrXam1rva8XgxYlVLxXosgZbLxnLv26KaxCWMB+L7oe69dRgjRLXRW7utS0iLTAMi1WDk7uoTNMhBEiB6pNaOAjyx6PguYorV2ASilLgb+DVzppVjWA4OVUv2BfOA64IbGBTxJt1BrrZVSkzEqsKVeuj5EJEFMP08F8MeAsSLIwKiBZBRleO0yQohuobNyX5dyZCqY3NAoxlnzeDKvijq7ixCb2c+RCSG8qTV3AHOVUq8AiUDIkY1a608xvhF7hdbaCdwPfAZsB97VWmcqpe5WSt3tKXY1sE0ptRn4J3Cd1vr4ZuKOST0NctdBo9OmJ6azuXgzbu326qWEEF1ap+S+rqZPWB9MysSB6F70dezF5dZkFkgzsBA9TWvuAN4KXAX8HfhAKbUUyATGcewbsld4mnUXH7fthUavnwOe8+Y1T5A6Gba8A+X7jbuBGBXAD3Z/wL6KfQyMHujTywshuoxb6aTc15VYzVZ6h/Um1wmRlZsw4yIjt5yJ/WL9HZoQwotOeQfQ0+/uf1rrzcAPMCqNtwJpwLW+Dc8PUk8znnPXHd2UnpAOIM3AQgSQgMt9jaRGpJJn0ihXA1Miy8iQfoBC9DituQN4lNa6EviLj2LpGhJHgC3c6Ac45hoA+kb2JSYohu+LvueqIVf5OUAhRGcLiNzXSGpEKp+XbANgZkwhLx0o929AQgiv60rzAHYNJjOkTGwyElgpxdjEsWwu3nySA4UQomdIjUilwlFNpSWY8UF55JfXUVRZ7++whBBeJBXA5qSeBoWZ0FB1dFN6Qjo5lTmU1Zf5MTAhhPC9tAjPVDCJg+jnzAZg0wGZEFqInkQqgM1JnQzaDfkbj26akDQBgPWH1vsrKiFED6WUulAptVMptUcp9XAz+5VS6p+e/VuUUuN9GU9KRAoAuTHJRJRvx2ZWbJJmYCF6lFZXAD0J6Cal1GOe92meufh6npRJgIL9q49uGhU/ighbBCvzV/ovLiFEp/N17lNKmYHngYuAEcD1SqkRxxW7CBjsecwB5nrr+s1Ji0xDodgXGoGqLeWsXg427Zc7gEL0JG25A/hvYApwved9FUbS6nmCo6D3GMj57ugmi8nClN5TWJm/Em9PPSiE6NJ8nfsmA3u01tlaazvwNjD7uDKzgde0YQ0QrZTq7cUYmgixhJASkcIe5QKMgSBb8iuwO2UuVCF6irZUAE/TWt8H1ANorQ8DNp9E5Sdb8yr409IdRgWv3zTIWweOuqP7pyZPpaiuiD3le/wYpRCik/k69yUDuY3e53m2tbWMVw2KHsTu+hIAxtnysDvdZB2s9OUlhRCdqC0VQIenqUIDKKUSgB71dTDrYAVzv97LjkNVRgXQZYe8Y33+zuhjrAMvzcBCBBRf5z7VzLbjmxlaUwal1Byl1Aal1Ibi4uIOBTU4ZjAHqvNoiO1PX/teAGkGFqIHaUsF8J/AAiBJKfUHYCXwlE+i8pNzhyehFHyeWQh9p4Aywb4VR/f3CuvFoOhBfFfw3UnOIoToYXyd+/KA1EbvU4CCdpRBaz1Paz1Raz0xISGhQ0ENjh6MS7vISRxMcPEW+kQFy0hgIXqQVlcAtdZvAg8Bf8RIPJdprd/1VWD+EB8exMS+MXyedcjTD3Bsk36AAFP7TGVT4SZqHbV+ilII0Zk6IfetBwYrpforpWzAdcCi48osAm7xDEg5HajQWh/0YgwnGBQ9CIDd0b2h4gDTkuF7GQksRI9xypVAlFJVNG1qUI32aa11pC8C85fzR/TiD4u3k3e4lpR+02DNXLDXgi0UgDOSz+DVrFfZULiBs1LO8nO0Qghf6azcp7V2KqXuBz4DzMB/tdaZSqm7PftfwFgjfRawB6gFbvPGtU+mb2RfLCYLe4KCADg3Io93yuM5VFFPr6hgX19eCOFjrVkLOEJrHdnoEdHo0aMqfwDnjUgCYFlWIfQ/C9wOYzCIx4SkCYRYQvgm9xt/hSiE6ASdmfu01ou11kO01gO11n/wbHvBU/nDM/r3Ps/+0VrrDd68fnOsZiv9Ivuxx1kFysxYtRuADftlMnwhegKZCPo4/eLDGJoUYfQDTDsdlLlJP8AgcxBnpZzFsv3LcLgdfoxUCCF8a3D0YHZX7IPEESRUbiPUZmb9PqkACtETnLIJ+Ail1M+a2VwBbNRaZ3gtoi7g/JFJ/PvrvRx2BhHTZxzs+7bJ/ov7X8xnOZ+xpmAN01Km+SlKIURnCKTcd7zBMYNZkrOE6uSzCM/6mAmpUazLkYEgQvQEbbkDOBG4G2PuqWSM2einAy8ppR7yfmj+c/6IXrjcmi+2F8KA6ZC/AeqOJb0zk88k0hbJ4n2L/RekEKKzBEzuO96RgSB7Y9OgvoKZSdXsOFRJRZ20fgjR3bWlAhgHjNda/1xr/XOMpJgAnAXc6oPY/GZUciTJ0SEs2XYIBp9nrAuc/fXR/VazlfP6nseXB76kzlnX8omEED1BwOS+4w2KMSqAe4I9g+CC96G1zAcoRE/QlgpgGmBv9N4B9NVa1wENXo3Kz5RSXDymNyt2F1MRO9aYEmb3F03KXDzgYuqcdXyd+7VfYhRCdJqAyX3HSw5PJsQSwh5XNdjC6d+wE4tJsS5H+gEK0d21pQL4FrBGKfVbpdTjwCpgvlIqDMjyRXD+dMmY3jhcms92lMCAGbDnC2i0BvCEpAkkhiayOFuagYXo4QIq9zVmUiYGRg1kd/le6DMOy8GNjEqOkoEgQvQAbZkI+nfAnUA5cBi4S2v9pNa6Rmt9ozeCUUpdqJTaqZTao5R6uJn9Sin1T8/+LUqp8d64bnNGJ0eRGhvCp1sOGs3A1YegcNvR/SZl4uIBF7MifwUHq306H6sQwo86I/d1ZcPjhpNVmoW7z3g4tI0pfcPYkldBvcPl79CEEB3Q6gqgUioIGAqEAVHALKXUY94KxLPW5vPARcAI4Hql1Ijjil0EDPY85gBzvXX9ZuLh4tF9WLmnhPI+ngmf9zRtBr5+6PUAvL79dV+F0WVorXG4HFTbqymrL6OotoiD1QfJq8ojtyr36COvKo+D1QcprCmkpK6E8vpyquxV1DnrcLgdaH3C8qVCdGm+zn1d3ZiEMVQ5qsiJ7wduBzMiC7C73GzOLfd3aEKIDmj1NDDAQjxTH+Cbfi+TgT1a62wApdTbwGyaNrHMBl7TRi1ijVIqWinV21dLIl0ypjcvfLOXpfvhuqTRRj/AM396dH/v8N5c2P9CPtj1AXeNuYuooChfhOFTDpfjaOUtvzqfQzWHKKkrMSpvDeVU2iupsldR66jFqZ1euaZFWbCYLFhNViwmS/MPZew3m8xYTBbMyoxZmTEp07Fnk/HceBsYd2cV6uh7pRQmTCh1dCEHlGdRh8bbjt93hKZppbW5SuzxZU5VvjXHtadcT3T876Ox35z+m2Z/h17m69zXpY2JHwPA5iAbA4DRjq3AKNbtK+O0AXF+jU0I0X5tqQCmaK0v9FkkxvQKuY3e5wGntaJMMnBCBVApNQfjLiFpaWntCmhkn0j6xoXyyZaDXDfoXFj9HNRXGINCPG4beRufZn/Ke7ve40ejf9Su63SWOmcd20q2saV4CzvKdrCjbAe5Vbm49LGmHKvJSkJIAnEhcSSEJjAweiARtgjCrGGEWEIIMgdhNVmxmq1HK10KhVIKrTUajVu7cWkXLrcLl3bhdDuPPbSzyXuH29Hk+fhyR85R76rHrd04tfPo+d1uz7N2H31ojsWABjfuo3EBTV83U6lqqbJ2fCWjuUpJ421tqZScrIJzshgCwanuGP/m9N90Rhi+zn1dWr+ofkRYI9hamc0ViSMIKVjDsF5TWLOvlB8z2N/hCSHaqS0VwFVKqdFa660+iqW5/7odn/1bU8bYqPU8YB7AxIkT23X7RCnFZWP78PzyPZSdMYNY97NGM/Coq46WGRo7lDP6nMGb29/klhG3YDPb2nMpn3BrN1tLtrIqfxWrClaxrXQbTrdxF69PWB+GxQ7jvL7n0T+qP2mRaSSHJxMXHBeQFQ0hTsLXua9LMykToxNGs6V4C/SdChlvceboaF5fl0+9w0Ww1ezvEIUQ7dCWCuCZwK1KqX0YzSAKY4nKMV6KJQ9IbfQ+BShoRxmvumJcMv/6ag8fFPfhzrAE2P5xkwogwG2jbuPOz+9k/o75/HDkD30Zzim53C7WHVrH5/s/Z/mB5ZTWl6JQjIwbyc0jbmZC4gTGJowlOjjar3EK0Y34Ovd1eaPjR/PS1peoTb+a0PUvcUHsIV52uvn+QDlTBkozsBDdUVsqgBf5LArDemCwUqo/kA9cB9xwXJlFwP2e/oGnARW+6v93xICEcNJTo/ng+0PcOexi2PIeOOrAGnK0zGm9TuOslLN4PuN5zu97Pr3De/sypGZlV2SzYPcCPs3+lOK6YkItoUxLmcY5qedwRp8zpMInRPv5Ovd1eWMSxuDWbjIj4pgEjHZtw2waxqq9JVIBFKKbass0MPuBSiAJ6Nvo4RVaaydwP/AZsB14V2udqZS6Wyl1t6fYYiAb2AO8BNzrreufzJXjk9lxqIr9STPBUQN7lzfZr5Ti16f9GoCn1j3VGSEB4HA7WLJvCT9c8kNmfzSbN7LeYGT8SJ45+xm+ufYbnjn7GWYNmCWVPyE6wNe5rzsYHT8agC3VByBuMMF5axidHMWqvaV+jkwI0V6tvgOolPoR8BOMZtcM4HRgNXCOt4LRWi/GqOQ13vZCo9cauM9b12utS8b04cmPs3irsC+PBEfB9kUwbFaTMsnhydwz9h7+tvFvfHngS85NO9dn8ZTXl/POznd4Z+c7FNcVkxqRyk8n/JTLBl5GfEi8z64rRCDqjNzX1cUEx5AWkcbWkq3Qbyps+5Cp6b/lxRX7qW5wEh7UlsYkIURX0JaVQH4CTAL2a61nAOOAYp9E1cXEhtmYMSyRBVuKcA+5CHYuBteJi6HfNOImhsUO4zff/Ybdh3d7PY79lfv5/Zrfc9775/FcxnMMiRnC8+c+zydXfMLto26Xyp8QvhGwua+xMQlj2Fy8GZ02FRoqmRlbjNOtWS/LwgnRLbWlAlivta4HY2JUrfUOjMlRA8JV45MpqmpgW9R0YyqYfd+eUMZqsvKPGf8g2BLMPV/cw6GaQx2+rtaajKIMHlz+IJcuuJQPd3/IrAGz+Gj2R7xw3guclXLW0fnuhBA+EdC574jR8aMpqSvhYJIx9csox1ZsZhOrpRlYiG6pLTWHPKVUNPARsEwptRAfj8DtSs4ZlkRcmI0Xc9PAFg6ZC5ot1ye8D3NnzqXGUcPdy+5mf+X+dl3P4TL69920+CZuXnIz6w+t50ejf8TnV3/OE2c8wcDogR35OEKI1gvo3HfEpF6TAFhTtQ/iBmPN+ZrxfaNZuafEz5EJIdqjLYNArtBal2utHwd+A/wHuNxHcXU5NouJqyemsHRXBXWDLoashcZo4GYMjR3KP8/5J8V1xfzg4x+wYPeCVi+Btvvwbp7d+Cwz35/JQ98+RHlDOY+e9ijLrl7GA+MfkGZeITpZoOe+IwZFDyIxJJGV+SuN9dFzvmN6/3AyCyopqQ64BVKE6Pba1Xaotf5Ga71Ia233dkBd2XWT0nC5NUstM6ChEnZ82mLZSb0m8cFlHzA6fjSPrXqMKxddyauZr3Kg8gB2l/Fjc7ldFNcW83Xu1/xtw9+4/KPLuXLRlfwv83+kJ6TzwswX+PiKj7lu2HWEWkM76VMKIVoSqLkPjNkOpvSZwpqDa3ANPAec9VwYvgeAb3cFXJdIIbo9GbrVBv3jwzhjYBx/2xXE5VGpqIy3YPTVLZbvFdaLl85/iYV7FvL+rvd5ZsMzPLPhGQAibBFU26uPLkdmMVkYmzCWR4c9ysy+M+VOnxCiy5maPJWFexeyLTyasdZQ+patJD78Ar7eWcyV41P8HZ4Qog2kAthG101O44H533NgwmX0zZoLlQchsuWJn03KxBWDr+CKwVeQXZ7N5uLNHKo9xOH6w0QFRREbHMug6EGMjh9NsCW4Ez+JEEK0zZTeU1AoVhVtYGy/aag9X3DWkJv4akcRLrfGbJJlJIXoLqQC2EYXjEwiNszGvMrJ/EE/D1vegTMfbNWxA6IHMCB6gG8DFEIIH4kOjmZk3EhW5a/insHnwe7PuHhiLR9ucrA5r5zxaTH+DlEI0UptmQj6Z81srgA2aq0zvBZRFxdkMXPD5DSe/3oPj/WbRFDGWzD1J6Dkm68QPZHkvqbOSD6D/2z9D5UTHiISmOLehEn155udxVIBFKIbacsgkInA3UCy5zEHmA68pJR6yPuhdV03T+mLWSmW2s6Hkp2Qs8LfIQkhfEdyXyNn9DkDl3axtv4QxA0mNOcr0lOj+VoGggjRrbSlAhgHjNda/1xr/XOMpJgAnAXc6oPYuqykyGBmje7NkznD0SFxsPZFf4ckhPAdyX2NjEkYQ4Q1gq9zv4YhF0DOCs4fGMqWvHJKZToYIbqNtlQA04DGUx84gL5a6zog4P7qbz+zP6UNJrb0utyYDuZwjr9DEkL4huS+RqwmKzP7zuSL/V9QN/QicNm52PY9WsPynXIXUIjuoi0VwLeANUqp3yqlHgdWAfOVUmFAli+C68rSU6MZlxbNk4fOQCsTrHvJ3yEJIXxDct9xLh5wMbXOWr5xV0FUKikFS+kdFcxnmR1f/lII0TnashLI74A7gXLgMHCX1vpJrXWN1vpGH8XXpd05bQAbD4dQ0Od82PQ6NFT7OyQhhJdJ7jvRxKSJJIYk8um+xTBiNmrvV8weGsq3u4qptTv9HZ4QohVaXQFUSgVhLIAeBkQBs5RSj/kqsO7gwpG9GJgQxjMV50BDBWx8xd8hCSG8THLficwmMxf1v4jv8r+jfMj54HZwddhmGpxuvpFmYCG6hbY0AS8EZgNOoKbRI2CZTIp7pg9iQUkyZUlTYOWzYA/oH4kQPZHkvmZcPOBinNrJ5w2HIDqNAUWfExNqZak0AwvRLbRlIugUrfWFPoukm5qd3odnv9jFn+1X8XTNL2DdPDjzp/4OSwjhPZL7mjEsdhgDogbwyb5PuWbkFZhWP8/sIQ/ywfYi7E43Nku7lpoXQnSStlQAVymlRmutt/osmm7IajZx19kD+c1HdfxqwFnErPwHTLwDgiP9HZoQwjsk9zVDKcXlgy7nbxv/RtbpVzJipZPrQ9bySsMIVu0tYfrQRH+H2C1oramxuyipaqCs1k5tg4tauxO31rjcYDYZ/50JspgJDTITEWQhKsRKdKhNKtmiQ9pSATwTuFUptQ9j6gMFaK31GJ9E1o38YEIKc5fv4fe1V/LXum9h7QtwdsDNDytET+Wz3KeUigXeAfoBOcA1WuvDzZTLAaoAF+DUWk/s6LW94eohV/Pilhf536GV/KV3OoPz3ifM9jhLth6SCmAziqrq2ZxbQVZBJTsLK8kpqeVAWS3VDe0bOBMRbCExIojEiGB6RwXTKyqY3tEhpESHkBwTQkpMCKE2WfFVNK8t/zIu8lUQ3T0JBlvNPDhzCA99UM8vB55Pr+/+DmOvg+g0f4cmhOg4n+U+4GHgS63100qphz3vf9VC2Rla6xIfxtJmEbYIrhlyDa9mvcoDY24n9bPHuKt/CS9tM/HE7JEEW83+DtGv6h0uVu4p4csdRazZW0p2idF1VCnoGxvKgIRwJvePpXdUMPHhQcSEWQkPshJqM2M2KUxK4dYah8tNg9NNdYOTqnonFXUODtfYKa1uoLi6gcLKBtbuK6Owsh6nWzeJIT7cRmpsKGmeR2pMqPE+LpRekcGYTbKMaaBqdQVQa73fh3F06yQIcOX4ZF78di8/q7iGN/kOtfQRuO5Nf4clhOggH+e+2RjLygG8CnxNy7mvS7ppxE28vv11XtOHeTQokmvVMv5Wfy3LdxRx0eje/g6v0zldblbsKeHDTfl8kVVIncNFmM3MaQPiuHZSKhP6xjC8dyRhQe24M+d2gcsB2gXa7Xkcq/C5NZTUOskvbyCvooHcCjsHyhrILa9j4/7DfLLlIK5GFUSrWdEnOoTUmFBSYkJI9tw57B1lvE6MDAr4SnxPdsp/gUqp77TWZyqlqoDGXy2ONIN4o7Nbt0+CFrOJX5w/lHverGFr+l2M2fF32LkUhkrf8RNoDfUVUFsKdYehrhzqy41t9mpjPkVHLTjqwFkPzgZwNRiJz2U3kqC7cQJ0n3gNpQAFymQ8TCZQZs9rs/HaZG702uJ5mBq99jxU423mpsc3eTY1v10pz2vTsceR2Exmz2saxXsk9pM9H/2gjT5vo/dNtrXzd3TyAm0of4pznfJaJzlX2pSOfc6T6KTcl6S1PohxwoNKqZbaTTXwuVJKAy9qred54dpekRiayKUDLmVB9ifcPepyEjPeYXD4FXz4fX5AVQBLqhuYv/YAb649wKHKeqJDrVw5PpkLRvbitAGxBFk8FSlHHVTkQH4eVBVCdSHUlnjyYbmRBxsqjRkl7LXgrANHvZELT/G3ZAISPY9xjXd4cpwOt+JWFlzKjFObsWOmwW6h/qCJujwTtW4TDZhp0BZ2KjObMaPMVpTVhtlqw2yzYbZZsVitWKw2rDYrFpsNq9VqvLZaMJstaJMZrcxopYxnkwk3njyMQptMaBRamdBKGZErhfbkQn3kNQrtyY3GJ2+cK49+OLTWnuOPo1Sz6cWt3bjRuFx4njVutxuXBrfWuN0at3bjcmvc2lPeDWD0y9Ro3FqjtUZrI4Vp3Li18SvSxv8ZZTyfBI6UO17zv1PlOarJp/Lkur6Jgzl30iXNHtcWp6wAehKgAkZqrQ90+IrN83oSVErNwVi0nbS0zmmKvXBUL8amRHHP3tNYET8U05JfQr+pEBTRKdfvMhz1cHgflGVD+QHjUZEHVQeh6pCR8Fz2k5xAgTUUrMFg8TzMNjBbjYfJ2qgiZj1WMWpMuzH+Ej0PlwPc9cZ2t9P4Bu12e56dnocb3A5PBfNImUbfuN0ywW2X89tyn53aW7lPKfUF0KuZXY+24TRTtdYFnty4TCm1Q2v9bTPX6vS8B3DbqNtYtHcR/wo18birgYdSN3HvziAO19iJCbN1Whz+UFBexwvf7OXt9bnYnW6mDY7n8UtHcE4fO7aS7VD0JWTuNPJhWTbUFJ14EnMQOjSWupBoqoMjqA6LoTaqF7UWK7VmC7UmE3UK6oE65aZBa+q1i4ZGD7t2YddOHNqNw+3CoZs+nNptPHDj0m4caFzajQuNC3Djwo0LY6XDVrLTdJFE0SnOKojtnAogGF91lVILgAntvVBnJkEAT+VwHsDEiRPbcouh3ZRS/PaykVz571W8OfgX3Lz9bvj4QbjqZZ/dpfArlxNKdkHhNji0FYp3QvEOo8LX+FuLNRSiUiCyD/Q7E8ITISwRwuIhJBZCYiA4yhg5bQs3ypu66Og2t7tp5dDtPHYX0u06tv3os27aXON2YVRMj7xvVFE9WmFtZlvj5yOOfrXVTZ6aedOU59vyqZ2izAm7T1L+lNdrw99HJ/4teSP3aa1ntrRPKVWolOrt+eLbG2imdgBa6wLPc5EnnsnACbnPH3kPoH9Uf24ecTOvZL7C5WkTmF76Pso1gU+2FHDzlH6dFUanKq1u4J9f7uatdQcIp5ZfDy7lsvgCYss2oxdnUF1fTp7FTKnZTGlYHKURCRxOHUK5bQzlZjMVaCrcdipd9VQ5qql2VOPWnikmXRiPk6w0HWwOxma2HX02HqHYzDasJivBJisRJisWkwXrcc9mZTaeTWYsyoJJmTApExaT8dqszEeflVJH3yulMGHC7tLU2d3U2t3U2d3U213U2x04HC4a7E7sTidOpxunw4nL7cblcBp31dxu3G4X2q3R2m20WR/NaxqljbtlJo48g1Iasyc/WEzGNpMJT3zaeDaBSSlMCixKYTYrzMqYq9es1NH+lCbP68bbjhyrTE33o8BiMhn3IZXCZFLGs/KUB5TJZDTweH4nJmXCc+MSE8qTqjz38jx5S6nmsl3TLY3/cLXWxl1SfWxv77jBrftHegpt6YSwRik1SWu9vj0X6swk6E/j02K4ekIKT2bkM+vMXxC39k/QfxpMuNXfoXVcRT7kroW89ZC/EQ5uMZonwLhDFz8EUiZC+g0QOxBiB0BMXwiN6zkVYJMJTD37joY4QYdy3yksAn4IPO15Xnh8Ac+awyatdZXn9fnAkz6IpUPuGXsPS/Yt4XeYeedAAffHrOXD7xN6XAXQ7nTz0jeZfLfqfQaYN/PLpAPU6VJ21pj5Rb2ZwqBQinpFUc/xLT+HUQ3lRBJJTFAMkUGRxNsSGBAUSaQtknBrOBG2CMJt4YRZwgizhhFqDSXUGkqIJYRQi/EcZA4iyByE6ik5VfhNWyqAM4C7PSNxa/DuNDA9JgkC/OrCYXy27RA/KziHVwauRy1+CPqMg95j/R1a21QWQPY3kLMCcr6Dck9feEsw9E6HibcZz71GQ/xgo3lWiJ7Hl7nvaeBdpdQdwAHgBwBKqT7Ay1rrWUASsMDzH3wL8JbWeqkXru1VodZQHp78MD/9+qe8ljaC2wo/5F8HTmfnoSqG9uqe3WDK6svYW76X7PJs9h3eSeb+deTW5FFuduJKU2zzlDMTRWJQNL0iUhkZnsz00AQSQxOJC4kjPiSeuOA4YoNjiQ6KxmySQRWia+gS08DQg5IgQEJEED87fwhPfJzF0iue4KLi6+CNq+D2zyBuoL/Da5mzAfavhD1fwp4vjOZcMJpo+06F0+6GtNMgaTRY5C6YCBg+y31a61Lg3Ga2FwCzPK+zgW7x7fHctHOZmTaTfx74imGqnGus3/Ha6gH84YrR/g7tpJxuJzkVOWwv286Osh3sOryLXYd3UVZfdrRMiNtNP4eTMQ5Fr/B+jBgwhZR+M0iOGUxCaAIWk8y3J7oXpVs5As/TGfpGYIDW+kmlVBrQS2u9zpcBesPEiRP1hg0bOvWaLrfmBy+sIrukhi9v6U3cu7ONvm23fwZRyZ0ay0nVlMCupbBzCexdDo4aozm37xkw8FwYMB2SRnXdPnlCtJJSamN75g7trrnPH3kPoMZRw02Lb6Lw8F7mFjZwc/UzrPj1hUSFdI0WAq01B2sOsqV4C1tKtrCtZBs7ynZQ5+nOEmQOYlBYMkMaGhhUvJdBtZVE20NY2zAJ65iruPryqwi2dY3PIkRrtJT72lIBnAu4gXO01sOVUjHA51rrSd4N1fv8lQj3FFUz658rmD4kgRdnmlGvXgahsXDDu5AwtNPjOerwftjxCWz/BHLXGIMOIvoYU9YMvsDos2gL8198QvhAByqA3TL3+SvvAeRX53P9wquIqCtncu5EUs/7Hbef2d8vsTjdTnaW7WRT0Sa+L/qezUWbKaozupkHmYMYHjucUfGjGB49iBFlBfTbugBL/ka0OYisqLP406HxHIo7nT9fM5701Gi/fAYhOqKl3NeWe9anaa3HK6W+B9BaH1ZKSTvgSQxKDOdn5w3h6SU7+Gj0WK64eQHMvx5englX/w8Gtzguxru0Nppzt38C2xfBoS3G9qRRcNYvYegso3+idCoWojmS+9ooOTyZf573AvcuuZXlaZuIXfcBt57xc0ydsOqEw+0gsySTDYUb2HBoA98XfU+ts/ZoXJN6T2JswljGJoxlcMxgrLWHYf3L8M2voKYY4gZTduYT3LNtCGsLNLdM6cu8WcNlQmTR47SlAuhQSpnxDEZWSiVgfCsWJ/GjM/vz5fZCHl2wjTE/PpOBd35lVALfvBom3wnn/J8xBYq3uV2Quw52LoYdn0LZXmN7ymQ470kYfqkxSlcIcSqS+9ohPTGdN2a+yL1LbyMn5lWe/Dac/zvrR17vK2d32dlWsu1ohS+jOONoc+6g6EFcMuASJvaayPjE8SSFJR07sHgXfPxT2PKuMS/pkAvhtLv4tHoov/pwKxaz4uVbxjJzRFILVxaie2tLE/CNwLUY82G9AlwN/J/W+j2fRecl/mwKAThYUcesf6wgKTKYj+6bSrC7Dr58Ata9BOFJMP1XMOY6sIV27ELVxZC93BjAsXsZ1JUZkyb3PwuGXWzc6YsMnJn5hWisA03A3TL3+TvvHVH03bP837bnWB0SwqDoQTw4/kGmJk9td0WwoqGCzcWbySjK4Pui79laspUGlzFh3uCYwUxKmsSkXpMYnzSe2ODYE0+QvxG++7vRImIJgvQb4fR7ccQM4KnFO/jvyn2MS4vmuRvGkxwd0pGPLkSX0OE+gJ6TDMMYsaYw1u7d7r0QfacrJMLlO4u47X/ruWZiCn+6aowxh1P+Rvj0F1CwyRhpO/Z6GHwepJ1hrIJxMm4XlOyGgu8hfwPkrIRiz68jNA4GzTS+0Q461zd3GIXoZtpbAfQc2+1yX1fIewC4XRQ8fyFbarP4U8ogSpxlJIQkcEG/CxiXOI4RcSPoFdarSYVQa015QzlFtUXsr9zP3oq97D68m6zSLPKr8wEwKzPDYocxPmk8ExInMCFpAtHB0c3HoLUxw8G3zxhfkoOjYPIcmHwXhCdQXNXA/W9tYu2+Mm49ox+/njUcm0UGvomewRuDQLrlSDjoOonwmc928tzyPfx61jDmnOWZDkZr2L8K1s6FXZ8ZTRHmIGO6mNgBRmXOEgQoY73c2jI4nGM83J4le2zhkHa6MVXLgOnG3HwyaleIJmQUsP/YK4sp/dsU3CbIuvZPLMr/mu/yv8PZaHnFcGs4NrMNh8tBnauuyT6FIjk8meFxwxkRN4KxCWMZGTeSUOspWk20Nqa1+vYvxoC3sEQ4436YePvRJTq35JVz1+sbOVxr56krR3PFuBSf/AyE8BdvDAL5N56RcBgTMFcBHwBdeiRcV/Kz84awr6SGp5bsIC02jAtH9TIGXvSbajzsNcaEy/u+hdK9xh2++vXG/HxoCI6GkGhIHGY06SYMhT7jjUmYZXJRn3C63NQ6XNQ7XNTb3TQ4XTQ4jWe7U2N3uXG63Dhcbpxujcutcbo0rqMLioOryaLh+qTLuR9ddsh4cXTZIZM6sr3RUkSKJkscmRq/N3neK2P5IrPnfeOlkY4cf0IZz/FmdeyYpjFwdMkk4ISYeuAKBZL7OsgWmUDGGc8xY+VNTP78n5z3o4U02ELYfXg328u2U1JXQmVDJfWueoLMQQSbg0nwTKacEp5Cv6h+hFja0BzrdsH2j2HFX41Bb1GpMOsZGHcTWI+dZ8H3eTz8wVbiw4N4/+4zGJUsrSUicMgo4E5kMin+es1Y8svrePCd73kt7DQm92/UR8UWBkMuMB7CaxqcLkqq7ZRWN1Babae0xk55rZ3yWgfldXYq6pxU1jmobnBSVe+gpsFFdYOTWrsTh6vTllPtURpXFtWRdTOVcSen8TbUsUqvavyaxoPSj+2j0XaFYvUj53RGhVNynxece875/Hb9z3iy9K/oVy8h6KYFjIofxaj4Ud67iKMOMt6C1c8bA9/iBsFlz8GYa5tMXu9ya55esp2XVuzj9AGxPH/DeOLCg7wXhxDdgIwC7mTBVjMv/3Ai1764mlv/t47Xbp/MxH7NdFQWrVLvcJF3uI68w7UUlNdTUF7HwYp6DlXWUVTZQGFlPZX1zmaPNSmICrESFWIlIthKZIiF+PAwwoOshAWZCbVZCLOZCbGZCbYeeZiwmU0EWc1YzQqb2YTNYsJiMmE1exYSb7youOdO29HFw0+o3ByjtWdJdM9dQvfRu4bH7iK63aDx3Fl0G9tcnu1urXFr4y6k8Zqjr7Xn9ZE7k43LHDlGNyrf0vFH4nO5jx2rPWV1o/eN43drI2Z0M9uOfG595NzG9iM9U45so1FZGpXrpLuNkvu8wGYxccYlt3LHO/Cfon9g/e8FcPV/oU96x09engsb/gubXoXaUqNl5AevwPDLTmgdqah18OO3v+fbXcX8cEpf/u+SEVjN0mVGBJ62VAD/CSwAEpVSf8AYCfcbn0TVw8WHBzH/ztO5bt4afvjfdbwqlcCTsjvd5JTWkF1czd7iGvaX1pBTWsuB0loOVdY3KWtSkBQZTFJkMAMTwpkyMI7EiCASIoKICwsiNtxGbKiNmDAbEUGWTpmXTHR7kvu85JIxvXl3w7ncdiCcVxuew/zSOXDmg8Z8pNY2jrh1NhgrGGW8BXuWGduGzoLT7zH6Qzfz5WBXYRVzXttAfnkdT105musnp3X8QwnRTckoYD86VFHPDS+tIa+8jn9cm85FowN7iha3W7O/rJYdByvZcaiKnYeq2F1URU5pLS73sX+nCRFB9I8LIzU2lL5xoaTGhpASE0qf6BCSIoKwyLd50QwZBdw15JTUcP6z3zJ7aCh/iXgXMt4wZkEYd7MxJUv8kOYHsWkNZdnG/Ka7lhqDO+xVxipGY6+DCbdCTN8Wr7t02yF+/m4GITYLL9w0Xr50i4DhjVHAf9Ja/+pU27qirpoIAcpq7Pzo1fV8n1vOIxcN485pA3piJ/oTOF1udhdVszWvgm0FFWQWVLL9YCW1dhfgGRsTF8bgxHAGJ4UzKDGcgQnh9I8PIyJY1uEUbdeBUcDdMvd15bz3jy928/cvdvGP69KZHbMf1sw1JqzXLmOKlt5jjUqhNRTs1VB50Kj81ZUZJwhPgqEXGU28A6afdBCc0+XmL5/v5MVvshmbGs2LN02gV9QpptkSogfxRgVwk9Z6/HHbtmitx3gpRp/pyokQjH5sP393M59uPch5I5L4y9VjiA7tOX3MtdbkHa5j04HDbM6tYHNeOdvyK2hwGt2owmxmRvaJYkSfSIb3jmB470gGJ0YQYpORzcJ7OlAB7Ja5ryvnPYfLzfXz1pBZUMlH901laK8IqMiHvV8Z85oe2gYNVeCoNQbHRfSG6FSjb1/KREgc2aqprooq63ng7e9Zk13GTaen8ZtLRhBkkbwiAku7K4BKqXuAe4EBwN4jm4FwYKXW+iYvx+p1XTkRHqG15r8rc3h6yXYS/r+9ew+OqzzvOP792ZZlW7Il+YbvNgZDbIwveLBpMdQpLhCYlpiQaaEZUtIMZQKlJGE6tCETz3QC6TCkpDTp4FKC0xIgE3PLDCEUwi2AuVjY2MYXHIPv+H6XjWTp6R97ZG+EJOuyK3n3/D4zOzrn3bPnPK9W++jZ855LeSl3f2kKf3LWkO4Oq0OO1NazbPM+qjfupXrDPpZu2suuQ7UA9CnpweQRFUwZVcnU0RWcO7KCcYPKfCye5V17C8BCz32net7bceAoV97/O8pLe/H0LRcyIMd79l/4YDv/uOh9amqPcde8c7n6PF/fz9KpMwVgBVAF3A3ckfXUwYjYk9Mo8+RUT4TZ3t+8j9seX8r6nYe5cspw7rxyIsMrTu3bEW3bf4QlG/Yef3yw9QDHkmP2xg8uY/qYKqaPqWTa6ErOHtbfZ9xZt+hAAVjQua8Q8t47H+/h2gWLmTa6koduOD8nReDBo3Xc/evV/PytjUwaPoB/v3Y6Zw4tz0G0ZoWpMwXg+cCmiPgkmb8e+BKwAZjvRJh7nx6rZ8Er67n/pXUAXDdzDN+YcwZDB3T/cSu1xxpY/ckBlmzYS/XGfVRv2MuWfZkbr/cp6cHUUZXMGFvFjLFVTB9TxcCy4hnKtsLWgQKwoHNfoeS9Z5dv49ZH32Pi8AEs/NrMDueMiOCFVTv47lMr2HHwKF+/aDzfvvQsD/la6nWmAKwG5kbEHkkXA48Bfw9MAyZGxDV5iDenCiURNrVpTw33//ZDFlVvoafE5ZOHcd2sMcw6fWCXnCgSEWzYXcP7W/azbNM+lm3ax/KsY/eGV/ThvDFVxwu+SSMGeO+enbI6UAAWdO4rpLz30uod3PS/SxhR2Zd7rpnS7jN0V2zZz13PruKN3+/m7NP686/XTGHa6Mr8BGtWYDpTAC6LiKnJ9I+BnRExP5lfGhHTch9ubhVSImzOht2H+enrH7OoejMHjx5j2IA+zJ00lDlnDWXG2CqqcrCX7cDROtbtOMS67YdY9UnmjNyVWw9wMLmIcmmvHkweWcH00ZXHh3RHVJ7aQ9Nm2TpQABZ07iu0vPf2R3v45uNL2br/CNdfMJab5pzR6uEv9Q3BK2t38LM3N/Dymp0MLOvNrX96JtfNGkvvXv4iataoMwXgCmBaRByTtBq4MSJebXwuInJ4H5/8KLRE2JIjtfU8t3Ibv1mxnVfW7uRIXeaSKeMHl3HG0HLGDyljREVfBpeXUtG3hNKSHpT07EF9Q1BX30BN7TH2H6lj7+E6th84yicHjrJpTw0b99QcP0kDoG9JT84e1p9zRgzg3JEVTB5Z4WP3rOB1oAAs6NxXiHnv8KfHuOc3a1j45scImD1hCBdPGMzogf0YVNabvTWZ3PX2R3t44/e72HWolqH9S/nrWWO5Yfa4nJ9IYlYMWsp9bbkTyKPAK5J2AUeA15IVngnsz1FwXwbmAxOBmRHRbNaSdDnwI6An8GBE/CAX2y8UfXv3ZN70UcybPoqjdfUs27SPdzfsZdmmfazfdZiX1+xo871re/fqwWkDShld1Y+5E09j7KAyzhxazoSh5YwZ2M9n5Zp1Qe6zP1RW2ov5f3EON1w4jkVLNrOoeguvrt35meWG9C9l9pmDmTvpNC47Z5i/nJp1QJuuAyjpAmA48HxEHE7azgLKI6K600FIE8ncW/MB4PbmCsDkXpxrgT8DNgPvANdGxAcnW38hfhPuiPqGYM/hWnYf/pT9NXXU1jdQe6yBnj1ESc8elJX2oqJvCVX9Mve/TcMFp80adeQ6gPnOfflUDHkvIth/pI6Ne2rYW1NHVb8SBpWXMqKij/OXWRt1Zg8gEbG4mba1uQgsWdcq4GQf6JnAuohYnyz7GHAVcNICMC169hBDkvvemlnn5Tv3WeskUdmvd1FdGN/sVFFI+81HApuy5jcnbc2SdKOkdyW9u3PnZ4cQzMzMzNKqTXsAc0HSC8CwZp76TkQ83ZZVNNPW4vh1RCwAFkBmKKRNQZqZmZmlQJcVgBExt5Or2AyMzpofBWzt5DrNzMzMUqdNJ4F0FUkv0/JJIL3InARyCbCFzEkg10XEyjasdyeZq/e3xWBgV1tjLnDua3FKS1/b28+xEVGYN9jugHbmPUjP3w2kp69p6Se4r61pNvedEgWgpHnA/cAQYB+wNCIukzSCzOVerkiWuwK4j8xlYB6KiO/nIZZ323umYKFyX4tTWvqaln52lTT9PtPS17T0E9zXjuiyIeDWRMSTwJPNtG8FrsiafxZ4tgtDMzMzMys6hXQWsJmZmZnlgAvAz1rQ3QF0Ife1OKWlr2npZ1dJ0+8zLX1NSz/BfW23U+IYQDMzMzPrOt4DaGZmZpYyLgDNzMzMUsYFYBZJl0taI2mdpDu6O558kvSxpOWSlkoq7DvGNyHpIUk7JK3Iahso6f8kfZj8rOrOGHOhhX7Ol7QleV+XJpdOKniSRkt6SdIqSSsl/UPSXnTva1dz3isOacl7kJ7cl++85wIwIakn8GPgC8Ak4FpJk7o3qrz7fERMK8JrJz0MXN6k7Q7gxYiYALyYzBe6h/lsPwH+LXlfpyWXTioGx4BvR8RE4ALg5uTzWYzva5dx3isqD5OOvAfpyX15zXsuAE+YCayLiPURUQs8BlzVzTFZB0TEq8CeJs1XAQuT6YXAF7sypnxooZ9FKSK2RUR1Mn0QWAWMpAjf1y7mvFck0pL3ID25L995zwXgCSOBTVnzm5O2YhXA85KWSLqxu4PpAqdFxDbIfKiAod0cTz7dIun9ZJikKIZ8skkaB0wH3iJd72s+OO8Vt7R9Poo29+Uj77kAPEHNtBXzNXIujIjzyAz93Czp4u4OyHLiP4EzgGnANuDebo0mxySVA4uA2yLiQHfHUwSc96xYFG3uy1fecwF4wmZgdNb8KGBrN8WSd8lt9oiIHWRuwzezeyPKu+2ShgMkP3d0czx5ERHbI6I+IhqA/6KI3ldJJWSS4CMR8UTSnIr3NY+c94pbaj4fxZr78pn3XACe8A4wQdLpknoDfwU8080x5YWkMkn9G6eBS4EVrb+q4D0DfDWZ/irwdDfGkjeNSSExjyJ5XyUJ+G9gVUT8MOupVLyveeS8V9xS8/koxtyX77znO4FkSU4bvw/oCTwUEd/v3ojyQ9J4Mt9+AXoBPy+mvkp6FJgDDAa2A98DngJ+AYwBNgJfjoiCPoi4hX7OITMEEsDHwN81HitSyCTNBl4DlgMNSfM/kzkepqje167mvFcc0pL3ID25L995zwWgmZmZWcp4CNjMzMwsZVwAmpmZmaWMC0AzMzOzlHEBaGZmZpYyLgDNzMzMUsYFoJmZmVnKuAA0MzMzSxkXgPYHJIWke7Pmb5c0v4tjOJQ1/UYO1jdf0u3NtFdK+kYut9VZkkZJ+ssmbQ9IulDSHEn/012xmRUz577u5dzX9VwAWlOfAldLGtzeFyojp39TEfHHuVxfE5XA8SSY52211SXAeU3aZgGLyVzl/r2uDsgsJZz7updzXxdzAWhNHQMWAN9s+oSkb0lakTxuS9rGSVol6SdANXCRpNWSHkyWe0TSXEmvS/pQ0sys9T0laYmklZJubC6Yxm/Ekm6StDR5fCTppaT9K5LeTtofkNQzaf+OpDWSXgDObqGvPwDOSF57T9a2xrWjD81uP+v5GY2xJvOTJb3ZQl9nAz8ErknWd7qkicDaiKgHpgIjJb0lab2kOS30y8zaz7nPuS9dIsIPP44/gEPAADL3UqwAbgfmAzPI3I+wDCgHVgLTgXFk7lF4QfL6cWQS6blkvmAsAR4CBFwFPJW1rYHJz75kbtw9qDGG7HiaxFdC5t6Ifw5MBH4FlCTP/QS4PivWfklf1gG3N9PXccCKpttqax9a2n6TbfQDtmTNPwHMbeX3/xwwOWv+W8DXkun3gPnJ9KXAa9399+KHH8XycO5z7kvboxdmTUTEAUk/A24FjiTNs4EnI+IwgKQngIuAZ4ANEbE4axUfRcTyZLmVwIsREZKWk0kwjW6VNC+ZHg1MAHafJLwfAb+NiF9JuoVMwntHEmSS6Q5gYBJrTRLDM+39HbSxD5e0sP3jIqJG0lFJlcB4oCoiXpBURiZp1gIvR8QjyUvOBtZkreIy4AZJvYBBwF1J+1IyN0I3sxxx7mtzH5z7ioALQGvJfWSGNX6azKuVZQ83mf80a7oha76B5G8u2YU/F/ijJFG8DPRpLSBJfwOMBW7JimlhRPxTk+VuA6K1dbXBSfvQ0vab8QHwOeC7wJ1J29XAL5Nk/jjwiKRBwP6IqEv60Q+ojIitkqYA6yKiNnn9ecCyjnfPzFpwH859jZz7ipiPAbRmRcQe4BfA3yZNrwJflNQv+QY3j8xwREdVAHuTBPg54ILWFpY0g8yQzFcioiFpfpHMMSNDk2UGShqbxDpPUl9J/ckMmTTnINC/E31oaftNrQRuABQRrydto4BNyXR98vN0YGvW6z4PNB5DMxU4XVKppHLge2T+UZlZDjn3tYlzXxHwHkBrzb0k3zgjolrSw8DbyXMPRsR7ksZ1cN3PATdJep/Mbv/FJ1n+FjLDGy8lQw7vRsTXJd0JPK/MGXh1wM0RsTj5ZrkU2EALyToidicHN68Aft3eDkTEB81tP9lmtpXAQuD8rLbNZBLhUk58EVsNDE7iuRH4AvDL5LmpwCPAG2SGW/6lydCTmeWOc18rnPuKgyI6u7fYzNor2ZPwH8BR4HdZx8FkL1MNzGocFjEzK3TOfacOF4BmZmZmKeNjAM3MzMxSxgWgmZmZWcq4ADQzMzNLGReAZmZmZinjAtDMzMwsZVwAmpmZmaWMC0AzMzOzlHEBaGZmZpYy/w+6p13SIk4IPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x324 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Utility function to place poles for the normalized vehicle steering system\n",
    "def normalized_place(wc, zc):\n",
    "    # Get the dynamics and input matrices, for later use\n",
    "    A, B = lateral_normalized.A, lateral_normalized.B\n",
    "    \n",
    "    # Compute the eigenvalues from the characteristic polynomial\n",
    "    eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "    \n",
    "    # Compute the feedback gain using eigenvalue placement\n",
    "    K = ct.place_varga(A, B, eigs)\n",
    "    \n",
    "    # Create a new system representing the closed loop response\n",
    "    clsys = ct.StateSpace(A - B @ K, B, lateral_normalized.C, 0)\n",
    "    \n",
    "    # Compute the feedforward gain based on the zero frequency gain of the closed loop\n",
    "    kf = np.real(1/clsys(0))\n",
    "\n",
    "    # Scale the input by the feedforward gain\n",
    "    clsys *= kf\n",
    "    \n",
    "    # Return gains and closed loop system dynamics\n",
    "    return K, kf, clsys\n",
    "\n",
    "# Utility function to plot simulation results for normalized vehicle steering system\n",
    "def normalized_plot(t, y, u, inpfig, outfig):\n",
    "    plt.sca(outfig)\n",
    "    plt.plot(t, y)\n",
    "    plt.sca(inpfig)\n",
    "    plt.plot(t, u[0])\n",
    "    \n",
    "# Utility function to label plots of normalized vehicle steering system \n",
    "def normalized_label(inpfig, outfig):\n",
    "    plt.sca(inpfig)\n",
    "    plt.xlabel('Normalized time $v_0 t / b$')\n",
    "    plt.ylabel('Steering angle $\\delta$ [rad]')\n",
    "\n",
    "    plt.sca(outfig)\n",
    "    plt.ylabel('Lateral position $y/b$')\n",
    "    plt.plot([0, 20], [0.95, 0.95], 'k--')\n",
    "    plt.plot([0, 20], [1.05, 1.05], 'k--')\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Explore range of values for omega_c, with zeta_c = 0.7\n",
    "outfig = plt.subplot(2, 2, 1)\n",
    "inpfig = plt.subplot(2, 2, 3)\n",
    "zc = 0.7\n",
    "for wc in [0.5, 0.7, 1]:\n",
    "    # Place the poles of the system\n",
    "    K, kf, clsys = normalized_place(wc, zc)\n",
    "    \n",
    "    # Compute the step response\n",
    "    t, y, x = ct.step_response(clsys, np.linspace(0, 20, 100), return_x=True)\n",
    "        \n",
    "    # Compute the input used to generate the control response\n",
    "    u = -K @ x + kf * 1\n",
    "\n",
    "    # Plot the results\n",
    "    normalized_plot(t, y, u, inpfig, outfig)\n",
    "    \n",
    "# Add labels to the figure\n",
    "normalized_label(inpfig, outfig)\n",
    "plt.legend(('$\\omega_c = 0.5$', '$\\omega_c = 0.7$', '$\\omega_c = 0.1$'))\n",
    "\n",
    "# Explore range of values for zeta_c, with omega_c = 0.07\n",
    "outfig = plt.subplot(2, 2, 2)\n",
    "inpfig = plt.subplot(2, 2, 4)\n",
    "wc = 0.7\n",
    "for zc in [0.5, 0.7, 1]:\n",
    "    # Place the poles of the system\n",
    "    K, kf, clsys = normalized_place(wc, zc)\n",
    "    \n",
    "    # Compute the step response\n",
    "    t, y, x = ct.step_response(clsys, np.linspace(0, 20, 100), return_x=True)\n",
    "        \n",
    "    # Compute the input used to generate the control response\n",
    "    u = -K @ x + kf * 1\n",
    "\n",
    "    # Plot the results\n",
    "    normalized_plot(t, y, u, inpfig, outfig)\n",
    "    \n",
    "# Add labels to the figure\n",
    "normalized_label(inpfig, outfig)\n",
    "plt.legend(('$\\zeta_c = 0.5$', '$\\zeta_c = 0.7$', '$\\zeta_c = 1$'))\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalue placement observer design (Example 8.3)\n",
    "\n",
    "We construct an estimator for the (normalized) lateral dynamics by assigning the eigenvalues of the estimator dynamics to desired value, specifified in terms of the second order characteristic equation for the estimator dynamics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "L =  [[1.4]\n",
      " [1. ]]\n"
     ]
    }
   ],
   "source": [
    "# Find the eigenvalue from the characteristic polynomial\n",
    "wo = 1          # bandwidth for the observer\n",
    "zo = 0.7        # damping ratio for the observer\n",
    "eigs = np.roots([1, 2*zo*wo, wo**2])\n",
    "    \n",
    "# Compute the estimator gain using eigenvalue placement\n",
    "L = np.transpose(\n",
    "    ct.place(np.transpose(A), np.transpose(C), eigs))\n",
    "print(\"L = \", L)\n",
    "\n",
    "# Create a linear model of the lateral dynamics driving the estimator\n",
    "est = ct.StateSpace(A - L @ C, np.block([[B, L]]), np.eye(2), np.zeros((2,2)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linear observer applied to nonlinear system output\n",
    "\n",
    "A simulation of the observer for a vehicle driving on a curvy road is shown below. The first figure shows the trajectory of the vehicle on the road, as viewed from above. The response of the observer is shown on the right, where time is normalized to the vehicle length. We see that the observer error settles in about 4 vehicle lengths."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAoAAAAE8CAYAAABQLQCwAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuNCwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8QVMy6AAAACXBIWXMAAAsTAAALEwEAmpwYAAB7nUlEQVR4nO3dd3xUZdbA8d+ZSSUJKST03nsNxYYgqFixKzawsdhd+7q67q66r66uvSJixV6xIip2QYr03gmdAAnpycx5/5gJRgyQCZPcycz5fryfmXvnlnMxeXLmuU8RVcUYY4wxxkQOl9MBGGOMMcaY2mUJoDHGGGNMhLEE0BhjjDEmwlgCaIwxxhgTYSwBNMYYY4yJMFFOB1Ab0tPTtXXr1k6HYYwJstmzZ+9Q1Qyn46grrCw0JjxVpyyMiASwdevWzJo1y+kwjDFBJiLrnI6hLrGy0JjwVJ2y0B4BG2OMMcZEGEsAjTHGGGMijCWAxhhjjDERJiLaAFKS53QEJoKUlpaSlZVFUVGR06GEjbi4OJo3b050dLTTodRp+cVlTodgjAkRkZEA5mSB1wMut9ORmAiQlZVFUlISrVu3RkScDqfOU1Wys7PJysqiTZs2TodTpxWWepwOwRgTIiLjEXBpIfz2mtNRmAhRVFREgwYNLPkLEhGhQYMGVqMaBAUllgAaY3wiIwGMSYSv/w1FOU5HYiKEJX/BZf+ewVFoCaAxxi8yEsDkZlCQDd/91+lIjDHGMSUeL7vyS5wOwxgTAiIjAYyuB30ugBnPwY6VTkdjTEj59ttv+fnnnw/pHImJiUGKxtS0BRvtSYgxJlISQIBj/gFRcfDF7aDqdDTGhIxgJICm7piftdvpEIwxISByEsCkRjD0b7ByKix8z+lojKlxp512Gv369aNbt26MHz8egC+++IK+ffvSq1cvhg0bxtq1a3n22Wd55JFH6N27Nz/88ANjxozh3Xff3Xue8tq9vLw8hg0bRt++fenRowcfffSRI/dlqi82ysW8LKsBNMZEyjAw5QaOgwXvwue3QtuhkNDA6YhMmPvXx4tYvCk3qOfs2rQ+d5/S7aD7TZw4kbS0NAoLC+nfvz8jR47kiiuu4Pvvv6dNmzbs3LmTtLQ0xo0bR2JiIjfffDMAL7zwQqXni4uL44MPPqB+/frs2LGDQYMGceqpp1oHjTokPtptNYDGGCCAGkARGSwi34vIIhF5XUQG1GRgNcLlhpFP+noDT/mb09EYU6Mef/xxevXqxaBBg9iwYQPjx49n8ODBe8fSS0tLC+h8qsodd9xBz549GT58OBs3bmTr1q01EbqpIfExbrbmFrM114bUMSbSBVIDOBG4EpgL9AMeFZFHVfXtmgisxjTqBkfeCN//F3qcAx2GOx2RCWNVqamrCd9++y1fffUVv/zyC/Xq1WPIkCH06tWLZcuWHfTYqKgovF4v4Ev6Skp8vUYnTZrE9u3bmT17NtHR0bRu3drG5qtj6sW4KQDmbdjNcd0aOx2OMcZBgbQB3KGqU1V1u6p+ARwH/KOG4qpZg2+G9E7wyQ1QvMfpaIwJupycHFJTU6lXrx5Lly5l+vTpFBcX891337FmzRoAdu7cCUBSUhJ79vz+e9C6dWtmz54NwEcffURpaeneczZs2JDo6GimTZvGunXravmuIoeIjBCRZSKyUkRur+TzC0Rkvn/5WUR6VeW8cdFRuF1iPYGNMQdPAEXkFRG5AfhRRP4hIuW1hsVAUL/+H6zQq7BffxHxiMhZ1bpQVCyc+gTkboTPbq12vMaEqhEjRlBWVkbPnj256667GDRoEBkZGYwfP54zzjiDXr16ce655wJwyimn8MEHH+ztBHLFFVfw3XffMWDAAGbMmEFCQgIAF1xwAbNmzSIzM5NJkybRuXNnJ28xbImIG3gKOAHoCowSka777LYGOFpVewL3AOOrcm6XQIeGidYRxBhTpUfALwC9gTTgGOBSEVkJtAEmBSuQCoXesUAWMFNEJqvq4kr2ewCYckgXbDkQBt8C3z0AbYdAr3MP6XTGhJLY2Fg+//zzSj874YQT/rDesWNH5s+f/4dt06dP3/v+//7v/wBIT0/nl19+qfSceXl5hxKu+aMBwEpVXQ0gIm8CI4G9ZaGqVhy3ZzrQvKon79U8hSmLt6Cq1oHHmAh20BpAVf1OVR9T1UtVtS/QDvgrcDcQH8RY9hZ6qloClBd6+7oWeA/YdshXHHwrtDwcPr0Rslcd8umMMSYImgEbKqxn+bftz2VA5dk+ICJjRWSWiMzavn07PVsks7uglA07C4MUrjGmLqrKI+DDpMLXRFX1qOoCVX1NVW8JYiwHLfREpBlwOvDswU62b6FXKXcUnPk8uKLg3UugrLjawRtjTJBUVi1X6ej1IjIUXwJ42/5OpqrjVTVTVTMzMjLo1TwFgHk2HIwxEa0qnUBGA7NF5E0RGSMiNdV1rCqF3qPAbap60BnN9y309iu5OZz2NGyeB1/eFUi8xhhTE7KAFhXWmwOb9t1JRHoCE4CRqppd1ZN3apxETJTLxgM0JsIdtA2gqo4DEJHO+BolvyQiycA04Avgp6okZFVQlUIvE3jTXyGZDpwoImWq+uEhXbnzSTDoKpj+NDTsApmXHNLpjDHmEMwEOohIG2AjcB5wfsUdRKQl8D5wkaouD+Tk0W4XXZvUt44gxkS4Kg8Do6pLVfURVR2BrzPIj8DZwIwgxbK30BORGHyF3uR9Ymijqq1VtTXwLnDVISd/5Y69B9oPh89uhtXfBeWUxhgTKFUtA67B19FtCfC2qi4SkXEiMs6/2z+ABsDTIjJXRGYFco0+LVOYn7WbUo83qLEbY+qOQGYC+ap8rClVLVTVz1T1WlXNDEYgVSz0ao47Cs6aCA3aw9sXwY6VNX5JY4ypjL987aiq7VT1Pv+2Z1X1Wf/7y1U1VVV7+5eAyuHMVmkUlXpZFORpCo0xdUcgA0HfCjwiIi+KSJOaCOZghd4++45R1Xf/fJZDEJcM57/l6xTy+tmQvyOopzcmFL300kts2vR7a4vLL7+cxYsXH+CIqlm7di2vv/56wMeNGTOGd98N7q+2+aPM1qkAzF63y+FIjDFOCeQR8BxVPQb4BPhCRO4WkWAOAxMaUlvDea9D7iZ4ZSQU7HQ6ImNq1L4J4IQJE+jadd9xhwNX3QTQ1LxG9eNonhrP7HVWvhkTqQKpAcQ/HMwy4Bl84/GtEJGLaiIwR7UcBKPegB0r4JVTLQk0ddJrr73GgAED6N27N3/5y1/weDyMGTOG7t2706NHDx555BHeffddZs2axQUXXEDv3r0pLCxkyJAhzJrla1KWmJjIbbfdRr9+/Rg+fDi//vorQ4YMoW3btkye7Guiu3btWo466ij69u1L3759+fln3xjFt99+Oz/88AO9e/fmkUcewePxcMstt9C/f3969uzJc889B/jmG77mmmvo2rUrJ510Etu2HfoQn+bg+rVKZdbaXahWOsKMMSbMVWUmEABE5EegLbAI38jzY4ClwPUicpSqjq2RCJ3S7hhfTeCbo+DV0+HijyA+xemoTF3z+e2wZUFwz9m4B5xw/wF3WbJkCW+99RY//fQT0dHRXHXVVdx7771s3LiRhQsXArB7925SUlJ48skneeihh8jM/HMzsvz8fIYMGcIDDzzA6aefzp133snUqVNZvHgxo0eP5tRTT6Vhw4ZMnTqVuLg4VqxYwahRo5g1axb3338/Dz30EJ988gkA48ePJzk5mZkzZ1JcXMwRRxzBcccdx2+//cayZctYsGABW7dupWvXrlx66aXB/Tczf5LZKpWP5m4ia1chLdLqOR2OMaaWVTkBBMYBi/TPXxevFZElQYwpdHQYDue+Bm9eAC+d7GsfmHygAfmNCQ1ff/01s2fPpn///gAUFhYyYsQIVq9ezbXXXstJJ53Ecccdd9DzxMTEMGLECAB69OhBbGws0dHR9OjRg7Vr1wJQWlrKNddcw9y5c3G73SxfXvmoJF9++SXz58/f274vJyeHFStW8P333zNq1CjcbjdNmzblmGOOCcK/gDmYfq3SAF87QEsAjYk8VU4AVXXhAT4+KQixhKaOx8OoN+GdMTBhmO/RcNM+Tkdl6oqD1NTVFFVl9OjRe+fxLXffffcxZcoUnnrqKd5++20mTpx4wPNER0fvnS/W5XIRGxu7931ZWRkAjzzyCI0aNWLevHl4vV7i4uL2G9MTTzzB8ccf/4ftn332mc1J64BOjZNIjI1i1rqdnNbHvtgaE2kCagO4P+WTloetDsPhsim+3sEvnghLP3U6ImMOaNiwYbz77rt729Pt3LmTdevW4fV6OfPMM7nnnnuYM2cOAElJSezZs6fa18rJyaFJkya4XC5effVVPB5Ppec9/vjjeeaZZygtLQVg+fLl5OfnM3jwYN588008Hg+bN29m2rRp1Y4llIiIS0QO9MXZUW6X0KdlCrPWWk9gYyJRII+AI1ujbnD51/DGeb5HwodfA8fcBVGxTkf2B2UeL0VlXryqqPpqXcof2sfHuImNclltSwTo2rUr9957L8cddxxer5fo6GgefvhhTj/9dLxe3+C/5bWDY8aMYdy4ccTHx/PLL78EfK2rrrqKM888k3feeYehQ4eSkJAAQM+ePYmKiqJXr16MGTOG66+/nrVr19K3b19UlYyMDD788ENOP/10vvnmG3r06EHHjh05+uijg/cP4SBV9YrIPBFpqarrnY6nMv1apfLY1yvYU1RKUly00+EYY2qRVLUHmIjEAmcCramQOKrqv2sksiDKzMzU8l6Nh6ykAL78O8yaCI26wxnjfclhDfF4ley8YrbkFrElp4ituUX+98VsyS0kO6+EghIP+cVl5JeUUVR64JH9o1xCQmwUCTFuEuOiSEuIoXH9OBolx9E0OZ62GQm0y0ikcf04XC5LFKtjyZIldOnSxekwwk5l/64iMjtYg9HXBBH5BugP/Arkl29X1VOdiGffsvDHFTu48IUZvHLpAAZ3PMCc6caYkFadsjCQGsCPgBxgNlAcyEXCSkw9OPkR6HA8TL4Gxg+Bo2+Dw66B6MrbPu1PQUkZW3J8Cd1Wf1K31Z/olW/btqcYj/ePSbrbJTRMivWP5VWPxFi3L6mLjSIhJor4GBcuEUQEAURAFQpL/YlicRl5xR7yikvJzith1rpdbMstpqTCtFDx0W66NEmiZ/MUerVIpm/LVFqm1bPaQ2MC8y+nAziQ3i1TcAnMWrfLEkBjIkwgCWBz/zzABqDTCLjyF/j0r/DNPTD7JRj+T+h+JqVeJTuvhO17/DV3uUVs/UOi53u/p6jsT6dNio2iUXIcjevH0a5dOo2TY301dPXjaOzf3iAxFneQa+dUle17ilm1PZ9V2/NYuS2PRZtyeGvmBl76eS0AzVLiObJ9Okd0SOfoDhkk17NHRsYciKp+JyKN8NUCAvyqqiEz0GFibBSdG9dnjs0IYkzECSQB/FlEeqhqkAc1C22qSmGph5zCUt9SULr3/e6CUrYn/Z3klsdw0uYnaf3eZSx87/94quQkvvRm4sG99zwugYZJvketbTMSOLxdg72JXvkj2Mb140iIdaZZpojQsH4cDevHcVi7Bnu3l3m8rNiWx6y1O/lpZTafL9zMW7M2EOUSDmvXgBO6N+H4bo1okBhabSGdpqpWWxpEdXWwYhE5B3gQ+BYQ4AkRuSXo01gegszWqbw3O4syj5cod1D6BRpj6oBA2gAuBtoDa/A9AhZAVbVnzYUXHE3ad9OL738Djyper+JRxeNVvP7XMo9SVOahsMRDYamXotLy9x4KSsoo9ez/3yg2ykVGUiyNEqM4me8ZmfMaaSWbyY9rwsYOF1DaYxTpjZuTXgO1dk7weJX5WbuZsmgrny/czLrsAqJcwrAuDTknswVHd8yI+D8ia9asISkpiQYNGlgSGASqSnZ2Nnv27KFNmzZ/+KwOtAGcBxxbXusnIhnAV6ray4l4KmsP/dHcjVz/5lw+ufZIujdLdiIsY8whquk2gCcEGE/IyC0sZdqybbhdgksEt0v87yHK5cLtEurFuKkXE0Vagpv4GDfx0S7io93Ex0SRHB9d6ZKSEE1SbFSFP/KDwfs3WP4FCdOfoeOCh2Dhw9DyMOh8MnQ+EVJa+RrlOU0VSgvA4xuS4/eYxNezeT+9m31DR6TSp2Uqt43oxJLNe/hw7kben5PFlEVbaZgUy/kDW3LhoFakR2itYPPmzcnKymL79u1OhxI24uLiaN68udNhVIdrn0e+2QRp+K1gGdjGV+M/fXW2JYDGRJAq1wACiEgv4Cj/6g+qOq9GogqyoPYCDsS2JbDoA1jyMWxb7NuW1ASaZ0Lz/tCwK6S2hpSW1R9OprQIinZD4W4o3HWQ97t86+XvvX9ug7iXOxbi6kNcCiQ1hvrNfLOgpLaGjC6Q0cn3eXkYHi/Tlm7jjV/XM23ZdmKiXJzRpxmXH9WG9g2TqndvxhxEHagBfBDoCbzh33QuMF9Vb3Minv2Vhcc89C1t0hN4YUz/So4yxoS6Gq0BFJHrgSuA9/2bXhOR8ar6RCAXjCgNu/iWoXdA9ipY+TVkzfQtSz6usKNAYiPfXMNxKb7Eyh3jq5UTF6jXN/xMaQGU5P/+WrgbygoPEID4zhWf6jtvfAokN//9fVyK7zr4vwSo+t6XFUFRLhTn+hLFPVtg3U+QuwnU8/vpk1v6ktmWg4huMZDjuvTguG6NWbktj4k/reG92Vm8NWsDJ/dsyvXD2lsiaCKK+B4NPI6vA8iR+JrNjFfVDxwNrBKHtWvAR3M3WTtAYyJIIG0A5wOHqWq+fz0B+KUutAF0rAbwQPKzIXsF7FoLO9dAbhYU5fy+eMp8iR8KiG/4meh6EJPw+2t5EhefWvn7uGRwufcbQsC8Hl+825f6aje3LoQNv0LuRt/n8WnQfrhv+rz2w9jpTWDCD6t56ee1FJZ6OLVXU246thMtG9i8oyY46kAN4GxV7ed0HOX2VxZ+On8zV78+hw+uOpw+LVMdiMwYcyhqug2gABWqf/D4t5nqSGjgW1oOcjqSqnO5oUE739K5wvTPuzfA+umw6mtY8SUseBtcUaS1P5Zbe53LZTcew/hfNvHKz+v4fMEWLjmiNVcf0576NvOACX/TRaS/qs50OpADGdQ2DYCfV2VbAmhMhAgkAXwRmCEi5Y8vTgNeCHpEpu5JaeFbep7tqyXcOAeWfAQL3oXln9Mgtj5/63kOV1w6mgdmKeN/WM07s7O48diOnD+gpc04YsLZUOAvIrIO30wgITl6QoPEWDo3TuKXVdlcPbS90+EYY2pBlRt7qOrDwKXATmAXcImqPhrMYERkhIgsE5GVInJ7JZ9fICLz/cvP/k4pJpS43NCiPxx3L/x1EVz0IXQ6Eea8QvrLR/Fg4d1MO7WYjg0TuPPDhZzxzM8s2pTjdNTGBJ2/DeA4oB1wDHAKcLL/NeQc3i6dmWt3UlzmOfjOxpg6L6DWvqo6W1UfV9XHVPW3YAYiIm7gKXzDzXQFRolI1312WwMc7f/2fA8wPpgxmCBzuaHdUDjjOfjrYjjmTti+lNZTLuENvZW3jtrBxp15nPLEj9zzyWIKSg7QK9mYOkZ9DawfUdV1+y5Ox1aZw9s1oLjMy2/rdzsdijGmFhw0ARSRH/2ve0Qkt8KyR0RygxjLAGClqq5W1RLgTWBkxR1U9WdVLZ+zaDpQJwcGi0iJGTD4FrhhAZz2DFKSz8CZ1zE97V/8s+N6XvhxNSc89gMz1+50OlJjgmm6iNSJsVUGtE3DJb52gMaY8HfQBFBVj/S/Jqlq/QpLkqrWP9jxAWgGbKiwnuXftj+XAZ/v70MRGSsis0Rklg3IG0Lc0dD7fLh6Jpw+Hre3mIvX3c68Vk/Q3rOSc577hXs/WUxRqT2GMmFhKL4kcJW/6coC/4gKIad+XDQ9mqfwy6odTodijKkFVX4ELCIPVGXbIaisJ0ClY9SIyFB8CeB+B1NV1fGqmqmqmRkZGUEK0QSNOwp6nQtXTYcTHyJ5zwpeKLqZ9xu/woc/zuXkJ35k6ZZgVjAb44gTgLbUgTaA4HsM/Nv63dYcw5gIEEgbwGMr2RbM6eGygBYV1psDm/bdSUR6AhOAkapqzyrqOnc0DLgCrvsNjriBPrnf8Ev92zgm71NOe/IHXpu+jkBmqzEmlPjb+7UAjvG/LyDEpoKr6PB2DSjzKjPX7jr4zsaYOq0qbQCvFJEFQKcKPXDni8gaIJiPMmYCHUSkjYjEAOcBk/eJpSW+mUguUtXlQby2cVpcMhz7Lxj3E9FNe3GH9zk+qXcPr3z0OVdNmkNOYanTERoTMBG5G9+Tir/5N0UDrzkX0YFltkoj2i38bI+BjQl7Vfkm+jq+RxaT/a/lSz9VvTBYgahqGXANMAVYArytqotEZJyIjPPv9g+gAfC0iMwVkRCb3sMcsoyOMPpjOH087aK283nc32m39DlOefRbZq+zWglT55wOnIpvDEBUdRMQsnMixse46dsylR+WWwJoTLg76EDQqpoD5ACjajoYVf0M+Gyfbc9WeH85cHlNx2EcJgK9zkXaD8P96U3cvPgtTiyZzV+fG8eFpxzLhYNa4RtizZiQV6KqKiIKe6fQDGlDOjXkgS+WsiWniMbJcU6HY4ypIdUdBmZPDQwDY8wfJaTDOS/DWRPpHJvNx7F3sOSTx7n1nXnWS9jUFW+LyHNAiohcAXwFPO9wTAd0TOeGAExbts3hSIwxNam6w8Ak1cAwMMZUrvuZuK6eQXSbI/lP9AscveBWLn1mKptzCp2OzJgDUtWHgHeB94BOwD9U9YmDHVeFWZE6i8gvIlIsIjcHM+aOjRJplhLPN0stATQmnAUyDMzZIpLkf3+niLwvIn1qLjRjKkhqhFz4Hgz/JydGzeK/2ddw++MT+XWNDRxtQpuqTlXVW1T1ZlWderD9qzgr0k7gOuChYMcrIgztnMFPK3fYtHDGhLFAhiO4S1X3iMiRwPHAy8CzBznGmOBxueDIv+K69Asa1Y/lBc9dTHvhDt6csdbpyIwJpqrMirRNVWcCNdI9/pjODSko8TBjtX3BMiZcBZIAln8VPAl4RlU/AmKCH5IxB9FiANFX/YR2OpHbot4g9ZPLePjjWXi9Nl6gCQuBzop0QNWZFemwtunERrnsMbAxYSyQBHCjvzHzOcBnIhIb4PHGBE98CtHnvYrnuP8w3P0bp868iH+/9CGFJfbIytR5VZ4VqSqqMytSfIybw9s1YNqybTYQuzFhKpAE7hx8Y/SNUNXdQBpwS00EZUyViOA+/Gpcoz+kWWwBN667koeffJRte4qcjsxEuPI5fytZqjIXcJVmRappx3RuyLrsAlbvyK/tSxtjakGVE0BVLQBWAceLyDVAQ1X9ssYiM6aKpM1g4q/+EU1ry99z/80nj17Lss05TodlIlv5nL/7LlWZC/igsyLVhqHlw8HYY2BjwlIgvYCvByYBDf3LayJybU0FZkxAUlqQfNXX7OxwNpd63ibr2TP5cfE6p6MyEUpV1x1oOcixB50VSUQai0gWcCNwp4hkiUhQh+VqnlqPjo0SrR2gMWEqkEfAlwEDVfUfqvoPYBBwRc2EZUw1RMeTdv7z5Bx9D0NkNilvnspH3890OioTwURkkIjMFJE8ESkREU9VBtBX1c9UtaOqtlPV+/zbni2fGUlVt6hqc/+4rCn+90EfmH9o54b8umYne4psLm5jwk0gCaDwe09g/O9tPi4TWkRIHnodJWe/Tjv3NgZ+fTavvv+hNWQ3TnkS3zSaK4B4fFNZHnQg6FAxrHMjyrzKt8uq1nvYGFN3BJIAvgjMEJF/isg/genACzUSlTGHKL7bCURd8SUxMbGcOW8sL014gpIyr9NhmQikqisBt6p6VPVFYKjTMVVVv1appCfG8MXCLU6HYowJskA6gTwMXIJvBPpdwCWq+mgNxWXMIYtu2oPU674np35HLtl4F+89fhO5hSVOh2UiS4G/I8dcEfmviPwVSHA6qKpyu4TjujVm2rJtNv+2MWEmoHH8VHWOqj6uqo+p6m81FZQxwSJJjWhy3VQ2ND2BUbkTmf7weWzKth7CptZchK+cvQbIxze8y5mORhSgE7o3pqDEw3fL7TGwMeEkkF7AcSJyo38O4PdE5K8iEleTwRkTFNHxtLjiDdb1uJ7jSr9my5MnsGyN9RA2Ncs/p+99qlqkqrmq+i9VvdH/SLjOGNS2Acnx0fYY2JgwE0gN4CtAN3wNmJ8EugCv1kRQxgSdCK3O/Dcbhz1Bd11GzEvHM3OO9RA2NUdVPUCG/xFwnRXtdnFc10Z8tXgrxWX2GNiYcBFIAthJVS9T1Wn+ZSzQsaYCM6YmNDvqYnLPeZ80Vx7tPjqNb778yOmQTHhbC/wkInf5n6DcKCI3Oh1UoE7u1ZQ9xWXWG9iYMBJIAvibiAwqXxGRgcBPwQ/JmJqV3vVoXGO/pig6hSN+upQvXn/ChokxNWUT8Am+sjapwlKnHNGuAQ0SYpg8t9ZnpDPG1JCoAPYdCFwsIuv96y2BJSKyAFBV7Rn06IypIUlNOhF7/fesf+YMRiy/ky+fWc3QsQ8RHeV2OjQTRlT1XwAikqCqdXZS3Si3ixN7NOHtWRvIKy4jMTaQPx3GmFAUSA3gCKANcLR/aQOcSNXmtqwSERkhIstEZKWI3F7J5yIij/s/ny8ifYNxXROZYpIa0O7GL1nU8CSO2zaRXx8+m7z8Ovs32oQgETlMRBbjm9INEeklIk87HFa1jOzdlOIyL18uss4gxoSDQMYBrPbcllXh7zH3FHAC0BUYJSJd99ntBKCDfxkLPHOo1zWRTaJi6XblJOZ3vJYjCr5m7SPHsm2rPeYKdbk5O/n5hVucDqMqHgWOB7IBVHUeMNjJgKqrb8tUmqXE88FvG50OxRgTBAGNA1jDBgArVXW1qpYAbwIj99lnJPCK+kwHUkSkSW0HasKMCD3Pv5fFhz9Ch9LlFD17DGuWzXM6KlOJ0pJiZrz1AGWP9OLwDeOdDqdKVHXDPpvqZFdal0s4vU8zflq5gy05RU6HY4w5RKGUADYDKhaUWf5tge4DgIiMFZFZIjJr+3bruWYOrutxl5I18i2SNJ/UN05k4c+fOR2S8VOvl7lTX2fz/X0YuOQ/bIlpxcqRHzsdVlVsEJHDARWRGBG5Gf/j4LrorH7N8Sq8/1uW06EYYw7RQRNAEdkjIrmVLHtEJDeIsUgl2/btmlmVfXwbVceraqaqZmZkZBxycCYytOs7jKIxX5LrSqHjlAuZ/bG1MnDaynk/svj+o+n905UAzD3yWbrc/j3t+9SJJ6njgKvxfVHNAnoDVzkZ0KFonZ5A/9apvDs7y3rOG1PHHTQBVNUkVa1fyZKkqvWDGEsWvmmSyjXHN4RCoPsYc0iatO5C8jXfsjy2B/1m386vL96Cer1OhxVxcrK3MOOJ0bR9/2SalqxlRpc7aHL7b/QePgpxhdLDiwPqpKoXqGojVW2oqhfiG0S/zjqrX3NWb89nzvrdTodijDkEoVSKzgQ6iEgb/8j55wGT99lnMr6haMQ/JmGOqm6u7UBN+EtOy6DDTV8wPflEBqwbz7zHz6GsuMDpsCKCt6yMX999CH2iH/12TGZGo3Nw3TCXgefeRnRMrNPhBeqJKm6rM07q2ZR6MW7emrn+4DsbY0JWQIM5iUgqvh64e+cAVtXvgxGIqpaJyDXAFMANTFTVRSIyzv/5s8Bn+IaeWQkUAJcE49rGVCY2Np4B103iu5fu4OgNz7Di4eE0HfcBCamNnA4tbC2f9TWuz29hgGcVi6J7EH/awxzWbYDTYQVMRA4DDsc3FVzFmT/q4yvf6qzE2ChG9m7GB79l8feTupIcH+10SMaYaqhyAigilwPX43vsOhcYBPwCHBOsYFT1M3xJXsVtz1Z4r/ja0xhTK1xuF0dfdj/ff9CWgXPvYOcTgym68A0atLUhKINp17YsVr1xM5m7Pmcbaczs9xCZJ11Wlx717isGSMRXxlac+SMXOMuRiILogoEteePX9XwwJ4sxR7RxOhxjTDUEUgN4PdAfmK6qQ0WkM/CvmgnLmNAy+PSxzExvRauv/kK9V0aw5diHaXzEhU6HVed5y0qZ8/7/6LT4MXpqMT81uYie599D//qpTod2SFT1O+A7EXkpGOOkhpruzZLp1SKFSTPWM/rw1ohU1j/PGBPKAvl6XaSqRQAiEquqS4FONROWMaGn/1HHs+OCKSyjDY2nXs2aSX8FT5nTYdVZq+Z8w9r7B5C5+P9YE9OJjaO+5ohxT5JUx5O/fRSIyIMi8pmIfFO+OB1UMFwwsCUrtuXxy+psp0MxxlRDIAlgloikAB8CU0XkI6wHrokwXTt2IuPaL/kk7mTarJjIuseOoyx3m9Nh1Sm52ZuZ8/gFtJt8Oollu/k183/0uP0b2nTu43RoNWESsBTf1Jn/Atbi6/BW553aqykNEmKY+OMap0MxxlRDlRJA8dXvX6equ1X1n8BdwAvAaTUXmjGhqVmDZI69+RXeafF3GuXMZ/djh7N72Q9OhxXy1FPGbx88jD6RSY/sz/mp4Shib5jNgJMvr8tt/Q6mgaq+AJSq6neqeim+9tN1Xly0mwsGteLrpdtYs8Pm0DamrqlSqevvfPFhhfXvVHWyf8o2YyJObJSbsy+7lR8GT6KgTEh841Q2Tf4XeOvkLF81bv2CH1h9/yD6zPsX66PbsPasLzjiqmdJTklzOrSaVup/3SwiJ4lIH3wd6cLCRYNaEe1y8eJPVgtoTF0TyNfu6SLSv8YiMaYOOnbY8eRfMo1v3EfSdM7DbHr8WLy7bZqscvm7tzPn6TE0f/cU6pdu56de99Pt9u/p0KPuDe1STfeKSDJwE3AzMAG4wdGIgigjKZZTezfl7VkbyM4rdjocY0wAAkkAh+JLAleJyHwRWSAi82sqMGPqii6tmzPwxvd4udHtJO9aSP5jg9g1+32nw3KUekqZ98H/KH20Dz23fsRP6WfhvnYWR5x+JS532D7u/RNV/URVc1R1oaoOVdV+QDun4wqmcUe3o7jMy0SrBTSmTgmkJD4BaItv3L9TgJP9r8ZEvOSEGC4edzvfDX2f9d50Uj++hPUvXoIW7nI6tFq3+peP2PCffvSa92/WR7Vi2chPOOraCaQ1sDm5/W48+C51R/uGiZzQvTGv/LyOnMLSgx9gjAkJgSSA64GjgNH+ca0UsCkRjPETEU4cciRxV37Du/Fn03Tth+Q81I+cufvOaBiedqxdwOKHjqftlIsRTzE/9XuUbn/7gW59j3A6tFATdoPmXTWkPXuKy3jl57VOh2KMqaJAEsCngcOAUf71PcBTQY/ImDquXeM0Trt5PB/2e4UtZQkkf3gRG54/D80Nz1GT9mxby/xnxpDy4mBa7JnHNy2vJeXm2RxxyiW4I+hxbwDU6QCCrXuzZIZ3acjzP6wmp8BqAY2pCwIpnQeq6tVAEYCq7sI33ZExZh9RbhdnnXoKUeO+482EC2iYNZWiR/qy9Yv/Qll4dJ4v3LmZ+c+PI+bpTDpvmcyPKaey+/IZHHPpvSQlJjodnqNEZI+I5Fay7AGaOh1fTbjpuE7sKS7j2e9XOR2KMaYKAkkAS0XEjf/bq4hkAN4aicqYMNG+SRpn3/QUXw75iF+1K42m38f2BzPJm/8xaN2sCCrO3c6Cl2+Ex3vRNestZiQOY82oHxjy15dp0aKV0+GFBFVNUtX6lSxJqhrIFJx1Rpcm9Tm1V1Ne/GkN23KLnA7HGHMQgSSAjwMfAA1F5D7gR+D/aiQqY8KI2yWcMvRIet7yBa+0eYC8wmIS37+QLQ8fReHyaU6HV2V5W1ezYMI4vA93o9vqicyOO4wlZ0xl8M1v0alzN6fDCysiMkJElonIShG5vZLPRUQe938+X0T6OhHnvv46vCMer/K/L5c7HYox5iCq/E1UVSeJyGxgGL5GzKep6pIai8yYMJOaEMPFo8exdOPZvPz+kxy34yXiXz+NTan9ST32ZuK7HA8SYv0DVNm+5Hu2ff0UnbKn0lmFnxOOIXHoXzki83Ak1OINA/4nLU8BxwJZwEwRmayqiyvsdgLQwb8MBJ7xvzqqdXoCYw5vzYQf13DhoFb0aJ7sdEimmlSV4jIvuUWl5BWVkVdctve1uMxLSZmXEo//1f++fHuZx4tXwataYfGd0+vlj+uqePz7ln9eTuT3IlGQvd2nBPaWPYLvS7ZLhCiX4Hb7X13lry7cLnC7XPtsL9/fhVsqbHP/8dgol+Da9xiXEOVy7d3fVenxvs/3vV4olZlVTgBF5AFVvQ3fvJb7bjPGVFHnZg3ofO3dzFk1lqkfPcKxO98h/u1z2R7fhpgjryW5/yiIqedojN6CXayc9jL15r5E89I1xGo836acQdMRN3F0l66OxhYBBgArVXU1gIi8CYwEKiaAI4FX/LM0TReRFBFpoqqbaz/cP7p2WAfen7ORf328iHfGHRZSf/AinderbM8rZtPuQjbnFJGdV8yOvBKy84vJzivxLfnF7MwvYU9RGWXewJupxLhdviRIBBFwucrfCy4Bl/9VRHC5ytd//0zEl+wpureVjOJLFsvfs892r4LHq3i8SplX8Xi9/lfd++qpxr3UBJfwe/K4T3Lpdskfk1t/AiyU/7v4PhOAfderIZC2KMcC+yZ7J1SyzRhTBX3bNaHvjf/ltzU3MeWLiQzY/AZdp95I4Vd3srP1iTQ6agxRbY6stVpBLckna8YHFMx5mza7fqIjZSylDVPa/o3ux1/G8EY2jl8taQZsqLCexZ9r9yrbpxnwpwRQRMYCYwFatmwZ1EArUz8umluO78Tt7y/gndlZnJPZosavaX63K7+E1TvyWb09j7XZ+WzcVcim3UVsyilkS07Rn5I6EUiJj6ZBYiwNEmLo3Lg+aQkx1I+PIjE2msS4KJJio0iKiyIxNoqE2Cjiol3EuN3ERLl+X9wuot2hVcNVUXmiWOb1/p4YeiokiFq+7v1D4lieUHq8+z+2zOvFq0qZRys9tsyreP+0vXx/r+/a/nVfUguK4v8P1Yrbf1/Hv58qfFWNf5ODJoAiciVwFdB2n5k/koCfq3FNY0wFfdo0os+Vf2P9jut4ZeqHpCx/h2NWf0LUmnfJiW5IXsuhpPc5hdgOQyE2iL1rVSnZvoINMybjXfEVLXJn04IStmoK3yWfSmzf8xh4xDA6R4dln4VQVtlf0H2rL6qyj2+j6nhgPEBmZmatVIOck9mC9+ds5L5PlzC0U0MykmJr47IRJTuvmEWbclm8OZeV2/JY40/6dlUYhifKJTRJiaNJcjyZrVJpmhJPk5R4mib7tmUkxZJaL5qoCBiuSURwC7hdbqdDqRHPXhT4MVUp2V8HPsfX4aNiY+Q9qroz8EsaYyrTMj2Bi0ddQKlnFD8uXsfaH9+i6ZZvOHzlZGJXvUUZUWQndqCscW/qtx1AUsuekNwCEhsevJawOA/PzrXs2riM3avmwOY5ZOQuItmbQztgjTbmu6QTcXc9iX5HncKxSfG1cs+mUllAxWqz5sC+g0hWZR/HuFzCf87owYmP/cA/P17EU+eHRB+VOklV2ZxTxIKNOSzamMOiTbks2pTLlgo9rTOSYmmbnsCI7k1ol5FA24wE2qQn0iI1PiKSO1M9B00AVTUHyAFGiUgqvkbHceDLqFX1+5oN0ZjIEu12MbRHG+hxO0WltzBz5RbW/PYN0Wun0TJ3KT32fEjSyjf27l8iMeyJzqDUXQ+POxaPOw7xenCX5RPlKSCubA/1vTm4gXQgTYWVNGNmXH+KGvahQc/j6d2rL21iwvObcR00E+ggIm2AjcB5wPn77DMZuMbfPnAgkBMK7f8qat8wkeuHd+DBKcs4tstGTuvTzOmQ6oQyj5clm/cwa91OZq3bxey1u/Ymey6BdhmJDGqbRremyXRrWp+uTeuTUs+G5DWBC6QTyOXA9fi+ac4FBgG/4Jsb+JCISBrwFtAaWAuc4x9ouuI+LYBXgMb4xh8cr6qPHeq1jQllcdFujurSjKO6XARcRF5xGYuydrFu5UKKNy9FcjYQV7CJhJLtxBYXEaPFxLAHLy6KXUmUuhtSEp1IcUJzSGtNfEY7GrXrQZdWTekYbQlfKFLVMhG5BpgCuIGJqrpIRMb5P38W+Aw4EVgJFACXOBXvgYw7uh3fLtvGXR8upF+rVFqkOdu5KRSpKsu35vHjyh38tHIHM1Znk1/iAaBJchyZrVPJbJVKzxYpdGlcn3j7omaCRLSKg9GKyAKgPzBdVXuLSGfgX6p67iEHIfJfYKeq3u8f8yp1397FItIEaKKqc0QkCZiNbyiaxZWc8g8yMzN11qxZhxqmMXWCx6t7e9mFOxGZraqZTsdRVzhRFm7YWcCJj/1A24wE3vrLYcTZFw9yCkr5dvk2pi3dxo8rs9mRVwxA2/QEDm/fgP6t08hsnUazFGuKYaqmOmVhIK27i1S1SHzduWNVdamIdAowxv0ZCQzxv38Z+JZ9ehf7H29s9r/fIyJL8PV6O2gCaEwkcbvCP/EzdUeLtHo8eHYvxr02m399vIj/O6On0yE5Yl12Pl8t2cZXi7fy69qdeLxKg4QYjuyQzhHtfYslfKY2BZIAZolICvAhMFVEduFrnxIMjcrbr6jqZhFpeKCdRaQ10AeYcYB9anXoA2OMMZUb0b0xVw9tx1PTVtGpURJjjmjjdEg1TlVZtCmXzxZs5qslW1m+NQ+ATo2SGHd0W4Z3aUSv5im47AubcUggM4Gc7n/7TxGZBiQDVa4BFJGv8LXf29ffq3oO/3kSgfeAG1Q1d3/7OTH0gTHGmMrdeGwnlm/N41+fLKZxcjwjulf256DuW7ltD5PnbuLj+ZtZsyOfKJcwoE0a5/VvyfAujWjZwNpBmtBQrQG+VPU7ABFZDzxYxWOG7+8zEdlaPoq9v63ftv3sF40v+Zukqu8HHrkxxhgnuF3C4+f1YdTz07nuzd+YcHEmgzuGx+Di67ML+Hj+Jj6et4mlW/bgEjisXQP+MrgtI7o3tl66JiQd6givwaq7ngyMBu73v370pwv5WrS/ACxR1YeDdF1jjDG1JD7GzYtj+nP+hBlc/sosnr84k6PraBK4NbeIT+Zv5uN5m5i7YTcA/Vql8s9TunJizyY0TIpzNkBjDuJQE8BgPVq9H3hbRC4D1gNnA4hIU2CCqp4IHAFcBCwQkbn+4+5Q1c+CFIMxxpgalpoQw+uXD/QlgS/P5IEze3JG3+ZOh1UlO/NL+HyhL+mbsWYnqtCtaX1uP6EzJ/VoYsPcmDqlKlPB7aHyRE+AoHRZUtVsYFgl2zfhG+sKVf2R4NU4GmOMcUhqQgxvjh3EuFdnc+Pb81i9PZ+/HtsxJHuw5xSUMmXxFj5bsJkfV+ygzKu0zUjg+mEdOLlnU9o3DOL0jMbUoqrMBJJUG4EYY4yJHMnx0bx86QDu+nAhT05byex1u/jfOb1oGgJDoVRM+n5auYNSj9IsJZ7Lj2rLKb2a0LVJ/YgYZ9OEN5vl3RhjjCNiolw8cFZP+rdJ464PF3LcI99z64hOnD+gZa3PYbsjr5hvlm77U9J36RFtOLFHE3o2T7akz4QVSwCNMcY46qx+zRnYJo07PljAPz5axMs/r+Wvx3ZkRLfGNZYIer3Kgo05TFvmm5Fj/sYcVLGkz0QMSwCNMcY4rkVaPV65dABTF2/l/i+Wcs3rv9EiLZ7z+rfk1F5ND7mDhderLNu6h5lrd/Lrmp1MX53NjrwSRKBPixRuHN6RoZ0b0q2pPd41kcESQGOMMSFBRDiuW2OGdWnE1MVbmfjTGh6csowHpyyjY6NEDm+XTs/mybTLSKRh/VjSE2OJ3qeGML+4jM05hWzOKWLDzkKWbM5lyeZclm7ZQ15xGQBNkuM4sn06Qzo1ZHDHDNISbJw+E3ksATTGGBNS3C5hRPfGjOjemA07C/h84Wa+X76DN2eu56WfvXv3E4Gk2CgU8HiVMo9S4vH+4VxJsVF0bpLEGX2b0btFCv1bp9E8Nd5q+UzEswTQGGNMyGqRVo+xg9sxdnA7yjxeVm3PZ8POArbuKWJbbjG7CkpwiRDlEtxuIa1eDI2T42iSHE/TlDiapViyZ0xlLAE0xhhTJ0S5XXRqnESnxjY6mTGHqnb72RtjjDHGGMdZAmiMMcYYE2EsATTGGGOMiTCiWtk0v+HFP5/xMqfjOETpwA6ngwiCcLiPcLgHCI/76GTTVVadlYUhJRzuIxzuAcLjPgIuCyOlE8gyVc10OohDISKz6vo9QHjcRzjcA4THfYjILKdjqGOsLAwR4XAf4XAPEB73UZ2y0B4BG2OMMcZEGEsAjTHGGGMiTKQkgOOdDiAIwuEeIDzuIxzuAcLjPsLhHmpTOPx7hcM9QHjcRzjcA4THfQR8DxHRCcQYY4wxxvwuUmoAjTHGGGOMnyWAxhhjjDERJqwTQBEZISLLRGSliNzudDzVISItRGSaiCwRkUUicr3TMVWXiLhF5DcR+cTpWKpLRFJE5F0RWer/f3KY0zEFSkT+6v9ZWigib4hInNMxVYWITBSRbSKysMK2NBGZKiIr/K+pTsYYqqwsDC1WFoaGSC8LwzYBFBE38BRwAtAVGCUiXZ2NqlrKgJtUtQswCLi6jt4HwPXAEqeDOESPAV+oamegF3XsfkSkGXAdkKmq3QE3cJ6zUVXZS8CIfbbdDnytqh2Ar/3rpgIrC0OSlYUOs7IwjBNAYACwUlVXq2oJ8CYw0uGYAqaqm1V1jv/9Hny/ZM2cjSpwItIcOAmY4HQs1SUi9YHBwAsAqlqiqrsdDap6ooB4EYkC6gGbHI6nSlT1e2DnPptHAi/7378MnFabMdURVhaGECsLQ0pEl4XhnAA2AzZUWM+iDhYWFYlIa6APMMPhUKrjUeBWwOtwHIeiLbAdeNH/+GaCiCQ4HVQgVHUj8BCwHtgM5Kjql85GdUgaqepm8CUIQEOH4wlFVhaGlkexstBxVhaGdwIolWyrs2PeiEgi8B5wg6rmOh1PIETkZGCbqs52OpZDFAX0BZ5R1T5APnXskaO/XchIoA3QFEgQkQudjcrUMCsLQ4SVhaHDysLwTgCzgBYV1ptTR6p39yUi0fgKvEmq+r7T8VTDEcCpIrIW3+OnY0TkNWdDqpYsIEtVy2sd3sVXCNYlw4E1qrpdVUuB94HDHY7pUGwVkSYA/tdtDscTiqwsDB1WFoaOiC8LwzkBnAl0EJE2IhKDr3HnZIdjCpiICL52FktU9WGn46kOVf2bqjZX1db4/j98o6p17puWqm4BNohIJ/+mYcBiB0OqjvXAIBGp5//ZGkYda7y9j8nAaP/70cBHDsYSqqwsDBFWFoaUiC8Lo2o0HAepapmIXANMwde7Z6KqLnI4rOo4ArgIWCAic/3b7lDVz5wLKaJdC0zy/yFdDVzicDwBUdUZIvIuMAdfr8rfqCPTIInIG8AQIF1EsoC7gfuBt0XkMnwF+tnORRiarCw0NcTKQocEqyy0qeCMMcYYYyJMOD8CNsYYY4wxlbAE0BhjjDEmwlgCaIwxxhgTYSwBNMYYY4yJMJYAGmOMMcZEGEsAjTHGGGMijCWAxhhjjDERxhJAY4wxxpgIYwmgMcYYY0yEsQTQGGOMMSbCWAJojDHGGBNhopwOoDakp6dr69atnQ7DGBNks2fP3qGqGU7HUVdYWWhMeKpOWRgRCWDr1q2ZNWuW02EYY4JMRNY5HUNdYmWhMeGpOmWhPQI2xhhjjIkwlgAaY4wxxkSYiHgEbIwxxhgfVaXE46WwxEN+iYfCkjJKPQqAiG8fQXC7IC7aTXy0m/gYN3FRblwucTByE0yWABpjjDFhpLDEw5od+f4lj3XZBWzdU8y23CK25haRW1SGx6vVOndctIv4aDf1YqJIjo/+41LP91o/PpqUCtvTEmJokBhDvRhLOUKJ/d8wxhhj6qhSj5cFG3OYs24XCzfmsGhTLqu251Exv2uYFEuT5DhapNWjX6tUUupFUy8mivhoNwmxbuJjoohxC+o/pvzQMq9SVOqhsMRDof+1qNRDQYmH/OIycgpLySksZdX2vL3vi8u8+401LtpFg4RY0hJi9iaFDRJiSEuI9b+Wb4slLTGGhBg3IlbjWFMsATTGmBokIiOAxwA3MEFV79/nc/F/fiJQAIxR1TkHOlZE0oC3gNbAWuAcVd1VG/djnKWqLNm8h2+WbuWX1dnMWbebwlIPAI3rx9GtaX1O6NGEjo0SaZueSOv0erVa81ZU6iHXnwzuLiwlp6CUnQUlZOeVsDO/mOz8Enb6l5Xb8sjOL6aotPKkMS7aRXpi7N4lIynmD+vpiTGkJ/ne14+LsmQxQJYAGmNMDRERN/AUcCyQBcwUkcmqurjCbicAHfzLQOAZYOBBjr0d+FpV7xeR2/3rt9XWfZna5fUqM9fu5OP5m/hmyTY25RQB0KVJfc7t34IBbdLIbJ1Kw6Q4hyP1tRmMi3bTsH7VYykoKfMniL4lO7+E7LxiduQVsyOvhB15xWTtKmDuht3szC+msqfXMVEu0hN+TwjTE2P8SeOfE8jk+GhLFrEE0BhjatIAYKWqrgYQkTeBkUDFBHAk8IqqKjBdRFJEpAm+2r39HTsSGOI//mXgW6qQAGr1mn0Zh6zZkc+7szfw4W+b2Li7kPhoN0d1SOeG4R0Z0jkjJBK+YKgXE0W9tChapNU76L4er7KrwJcU7tjjf80rZnuF9S05RSzcmEN2fkmlbR2j3UKDhFjSk3yPmxPjoqgX7aZejO9xeEKMr9NLvZgo6sX4EtrYKBcx/iXa7SLG7XsfW75e/rnbRbRb6kSCaQmgMcbUnGbAhgrrWfhq+Q62T7ODHNtIVTcDqOpmEWlYlWDyisuqHrlxhKry08psJv60hm+WbsMlcGSHDG45vhPHdWsU8R0p3C7ZW6NH4wPv6/UquwtL/cmiP0nMK9m7viPP90h6w64CCkt8bRsLSzyUePbfjrGqYtwVE0bZmxzGRLmJKV/fmzC6qG6+KEi1j43snyRjjKlZlRXN+1ZJ7G+fqhx78ABExgJjAdKbtwn0cFNLvF7li0VbeOyrFSzbuof0xBiuH9aB8we2pFEAj1PN71wu2dvhpGOjpCofV+rx7k0GC0rKKCjxUOrxUlLmpcT/WurxUlxW/l4pKfPs/azEo77XMi8lHg+lZbr3s2L/sSVlXopKveQWllFazYRTFRStds2+JYDGGFNzsoAWFdabA5uquE/MAY7dKiJN/LV/TYBt+wtAVccD4wFadOxuD4FDjKry/YodPDhlKQs35tK+YSIPntWTU3o1JS7a7XR4ESna7SI53kVyfLTToVSZ3BT4MSE1E4iIjBCRZSKy0t+wed/PO4vILyJSLCI3OxGjMcYEYCbQQUTaiEgMcB4weZ99JgMXi88gIMf/ePdAx04GRvvfjwY+qkowwXi0ZYJnzY58LnrhV0ZP/JXdBaX87+xeTLlhMGdntrDkz9S4kKkBrGJvuZ3AdcBptR+hMcYERlXLROQaYAq+oVwmquoiERnn//xZ4DN8Q8CsxDcMzCUHOtZ/6vuBt0XkMmA9cHZV4iktswrAUFBc5mH8d6t5YtpKYt0u7j6lK+cPbElslCV9pvaETAJIFXrLqeo2YJuInORMiMaY2qKqbN9TxIasDeRuW09p3k5UFVdUFHH1G1K/UUunQ6wSVf0MX5JXcduzFd4rcHVVj/VvzwaGBRpLddsameBZuDGHG96ay8pteZzUswl3n9w1oCFTjAmWUEoAq9JbrsoqNnxu2bJu/KEwJtLl5Jcw+9fvKFj4KRk759DJu5J+ku90WGGj1OPF61Wbz9UBqsrLP6/lP58tJS0hhhfH9Gdo5yp13jamRoRSAhiUHm97D6zQ8DkzM9OeexgTwuYtXc6Gr56j5/bJHCPb8CJsjm3LlvQRZDfqTL2MVsTVb4A7KhpPSRH5u7ZSsH0tcLfTodcpCmTnl5CRFOt0KBFld0EJt7w7n6mLtzKsc0MePLsXaQkxTodlIlwoJYBV6S1njAkj8xYvYcsn93F0/hf0klLWJPVhXe+baDHwTJolZez3uNS97ywBDNTmnEJLAGvRqu15XPrSTDbtLuTOk7pw2ZFt6sQgwSb8hVICuLfHG7ARX4+3850NyRhTE7Zk72L2pH8yNPsNuoqH1c1OpuXJt9GmaVenQwt7m3YX0rN5itNhRISfV+1g3KuziXa7eHPsYfRrlXrwg4ypJSGTAFalt5yINAZmAfUBr4jcAHRV1Vyn4jbGVJ2q8vUX79Nh+h2cJFtYlj6cluf+l04N2zkdWsTYtLvI6RAiwjuzNvC39xfQOj2BF8f0r9I0Z8bUppBJAKFKveW24Hs0bIypY3bnFfLDhFs4addrbItqzNZT3qJT7xFOhxVRRHyPgE3NmvDDau79dAlHtG/A0xf0q1MDCpvIEVIJoDEmPK1es4pdr47mFO8Cljc5hfZjnsUVl+h0WBEnxu2yGsAa9sy3q3jgi6Wc0L0xj53Xh5iokJpvwZi9LAE0xtSoOT9NoeWXV9BUCll71IN0HDbW6ZAiVrTbxSarAawxT3y9gv9NXc4pvZryyDm9iHJb8mdC10ETQBFpjW+Q0nb4ZuKYC3ysqutqNDJjTJ339Ucvc/icm9npboDn/A9p3b6v0yFFtGi3i027LQGsCU9NW8n/pi7n9D7NePCsnpb8mZBXlZ/Qj4Cl/D5NWy/gexF5SkRsLAFjTKWmvvYQR8+5gS2xbUi5ZhqNLPlzXLRb2Lan2GYECbI3fl3Pg1OWcXqfZjx0ttX8mbqhKj+lblV9QVW/Bnaq6hX4agPX4h9o2RhjyqkqP0y8g2NX3sPKxExa3vg1CWlNnA7L4GsDqAqbrR1g0ExZtIW/f7CAIZ0y+O9ZPXHbLCumjqhKAviVf3gW8M/MoaplqvogcFiNRWaMqXNUlW9fvJOj1j/Fb8nD6XDDJ7jjkpwOy/hF+zskbNhV4HAk4eHXNTu57o3f6NE8hacv6Eu01fyZOqQqnUBuBP4mIrOApv45dgvwJX/ZNRmcMaZu+eblexi2/knmpwyj1zVv4YqyfmahJMbtogjIsgTwkK3ansflL8+kWWo8L47pT70Y+1k3dctBv66oqldV7wMGA2OBxkA/YCFwQs2GZ4ypK35++38MW/s/FtU/ih7XvGnJXwiKjnLhdgkbdlpHkEORW1TKFa/MIsrt4uVLBti8vqZOqnIJraoFwGT/Yowxe835/EUGLbqHBfX60+Xqd5Ao+4MYigRokhxnj4APgcer3PDmXNZnF/Da5QNthg9TZ1mDBWPMIVk44yu6Tr+F5TFdaH/Nh0TFxjsdkjmA5qnxZO2yGsDqeujLZXyzdBt3n9qNQW0bOB2OMdVmCaAxptrWr1pMk88vYaerAU3+8h7xCTa7R0UikiYiU0Vkhf81dT/7jRCRZSKyUkRur7D9QRFZKiLzReQDEUnxb28tIoUiMte/PFvZeSvTIrUeG3ZaDWB1fDJ/E898u4pRA1py4cCWTodjzCGpcgIoPheKyD/86y1FZEDNhWaMCWW5u7ejk84mCi9y4Tskpzd1OqRQdDvwtap2AL72r/+BiLjxjbN6AtAVGCUiXf0fTwW6q2pPYDnwtwqHrlLV3v5lXFUDapFWj217iikq9VTvjiLUmh353PbufPq1SuVfp3ZDxIZ7MXVbIDWAT+Pr+TvKv74HX6FljIkwnrIyNjx7Dk08m9l43HiatOvpdEjVJiJuEfmqhk4/EnjZ//5l4LRK9hkArFTV1apaArzpPw5V/VJVy/z7TQeaH2pAzVN9j+g32owgVVZU6uHqSXOIjnLxxCib39eEh0B+igeq6tVAEYCq7gKspbcxEWjmxL/SrWgOs3vcRdfDT3I6nEOiqh6gQESSa+D0jVR1s/86m4GGlezTDNhQYT3Lv21flwKfV1hvIyK/ich3InLU/gIQkbEiMktEZm3fvn1vpwV7DFx19326hMWbc/nf2b1ommJtXE14CGSchlL/owoFEJEMwOYTMibCzP7iFQZteoUZaacy6MwbnA4nWIqABSIyFcgv36iq1x3sQH/tYeNKPvp7Fa9d2bNE3ecafwfKgEn+TZuBlqqaLSL9gA9FpJuq5v7pRKrj8c/alJmZqeU1gNYRpGo+W7CZV6ev44qj2jCsSyOnwzEmaAJJAB8HPgAaish9wFnAnTUSlTEmJGWtmEenX25lRXRH+owdH07toD71LwFT1eH7+0xEtopIE1XdLCJNgG2V7JYFtKiw3hzYVOEco4GTgWGqWj4bUzFQ7H8/W0RWAR2BWQeLt1FSHDFulw0FUwVZuwq47d359G6Rwq0jOjsdjjFBFcg4gJNEZDYwDN831tNUdUmNRWaMCSlF+Tl43ryQEokiafQbxMSFz6MwVX1ZRGLwJVEAy1S1NAinngyMBu73v35UyT4zgQ4i0gbYCJwHnA++3sHAbcDR/rFY8W/PwDc3u0dE2gIdgNVVCcjlEpqlxpNlg0EfkNer3PLOfLyqPDGqj03zZsJOQEP1q+pSYGkNxWKMCWGLXxhH77IN/DbkRfq1aO90OEElIkPwddJYi+8LbgsRGa2q3x/iqe8H3haRy4D1wNn+6zUFJqjqiapa5p9vfQrgBiaq6iL/8U8CscBUf23rdH+P38HAv0WkDPAA41R1Z1WDap4az3prA3hAL/28ll9WZ/PAmT1ssGcTlg6aAIrIHnztUcqf9ZS3TRFAVbV+DcVmjAkRv306nr47P+OHZpdw1NDTnQ6nJvwPOE5VlwGISEfgDXzTXlabqmbje2qy7/ZNwIkV1j8DPqtkv0ozbVV9D3ivunG1bpDAhxs2oqrh9Bg/aFZu28MDXyxlWOeGnJPZ4uAHGFMHHTQBVNWk2gjEGBOaNq9ZTIdf/8Hi6K4MuuS/TodTU6LLkz8AVV0uItFOBlSTWjWox56iMnYVlNo8tvso9Xi58e151Itx839n9rAE2YStKj8CFpEbK9mcA8xW1blBi8gYEzI8pcXkvz6aerhIufAloqPDNlmYLSIvAK/61y8AZjsYT41q3SABgLXZ+ZYA7uPZb1cxPyuHZy7oS8OkOKfDMabGBNKqNRMYh298qmbAWGAI8LyI3Br80IwxTpv3yq20L13O4sx7adq6k9Ph1KRxwCLgOuB6YLF/W1hqne5LANdl5x9kz8iyclseT3yzkpN7NuGEHk2cDseYGhVIJ5AGQF9VzQMQkbuBd/E1Rp4NhO2zIWMi0erZU+m9/mV+TD6JI06+xOlwaoyIuPA9yegOPOx0PLWhRVo8IrBmh3UEKef1Kn97fz7xMW7uPqWb0+EYU+MCqQFsCZRUWC8FWqlqIf7xqIwx4aEoP4e4T65hs2TQ7ZInw7odlKp6gXki0tLpWGpLbJSbpsnxVgNYwRsz1zNz7S7+flIXMpJinQ7HmBoXSA3g68B0ESkfx+oU4A0RScD3uMQYEyYWvnQDfb1bWXDsJHqlpjkdTm1oAiwSkV/540wgpzoXUs1qk57A2myrAQTYklPE/Z8t5fB2DTi73yFPt2xMnRDIQND3iMhnwJH4hoAZp6rlo85fUBPBRYriMg8bdxWybU8x2/1LfnEZhaUeikq9eLxeYqPdxEa5iI1y0SAxlsb142icHEfz1HiS4sK2s6JxwPKfPyRz+/v82PBcjjyybs/zG4B/OR1AbWvVoB6fzN/sdBgh4e7JCynxePnP6dbr10SOQAeCnk0Y94yracVlHpZs3sPSzbms3pHPqm15rNqex/qdBXj1z/u7XUJ8tBu3Sygp81JU5kEr2a9lWj26NqlP92b1Gdi2AX1apBBlo9abaijas5PUqTeyRprTe0xENIcrbwP4lL8NYMRok55ATmEpuwtKSKkXuT2Bpy3dxpRFW7l1RKe9nWOMiQSBDAMTC5wJtK54nKr+O/hh1X0er7Ji2x7mb8hhXtZu5mflsHRLLqUeXwYXE+WibXoCXZvW55ReTWnVIIFG9WNpmBRHRlIsSXFRf5p6SFUp8XjZkVfClpxCtuQUszY7n8Wbclm0KYcvFm0BICk2isPbN2BYl0ac0L2x1RCaKlvx0lV08e5i4wkTaJOQ6HQ4tUJVvSIyT0Raqup6p+OpLa32DgVTQO8ITQCLSj388+NFtMtI4PIj2zodjjG1KpAawI/wj/uHdfr4A1Ula1chczfsZt4GX7K3YGMOhaUewJeQ9WiezGVHtqVX82S6NU2mWWo8bldgjxpEhNgoN81S4mmW8ud5WHMKSvl51Q6+X7Gd75ZtZ8qirdz14UKO79aYM/o2Y3CHDFwBXtNEjtXfv0GP7M/5utElDBt0jNPh1LaIawPYuoFverO1O/Lp3SLF2WAc8vz3q1mXXcBrlw0kJsqempjIEkgC2FxVR9RYJHXInqJS5mflMHfDbn5bv5u5G3azI8+XE8dEuejWtD7n9m9Bz+bJ9GqRQpsGCbWSeCXXi+aEHr7xq1SVuRt28/6cjUyet4nJ8zbRNj2BsYPbcnrfZsRGuWs8HlN3FOVsJ3XabSyVtgwY/R+nw3FCxLUBbJFWzz8UTGT2BM7aVcBT367kxB6NObJDutPhGFPrAkkAfxaRHqq6oKaCEZERwGP4JkSfoKr37/O5+D8/ESgAxqjqnJqKB2BXfglLtuSyZPMelmzOZd6G3azcnre3LV7bjAQGd0ynT4sUerdIpXOTpD89unWCiNCnZSp9WqZy58ldmLJoK+O/X8Xt7y/gf1OXM/aotlx0WCvioi0RNLDi1evo7M1j1YmTSEqIvInvVfU7EWkFdFDVr0SkHr5yKGzFRbtpnhrPqu15TofiiHs+WYwg3HlSV6dDMcYRgSSARwJjRGQNvkfAAqiq9gxGICLiBp4CjgWygJkiMllVKw4xcwLQwb8MBJ7xvx6SgpIyNuwsZP3OAtbvLGDDzgLW7Mhn6ZZctub+/rQ7PTGWns2TOaVXU3q3SKFX8xSS64V++7rYKDen9mrKKT2b8POqbJ75dhX3fbaEl39Zy60jOnNKzybW8y2Crf7lI3rs+IyvGl7M8IFHOR2OI0TkCnyzG6UB7fDNdvQsMMzJuGpa+4xEVm6LvATw++W+JjK3HN+JppU0pzEmEgSSAJ5QY1H4DABWqupqABF5ExjJH8cYHAm8oqqKb0zCFBFpoqoHHMtg2+49/HPyIko9XgpKPOzML2F3QQk7C0rYnV/KnuKyP+yfGBtFqwb1OKJ9Ol0a16dzkyQ6N65f5wcHFRGOaJ/OEe3T+XHFDu77bAnXvfEbE39cw72ndad7s2SnQzS1rLQwl4Qvb2YtTel/cUQ++i13Nb4yaAaAqq4QkYbOhlTz2jdM5KdV2Xi8GnCb5LqqzOPl3k8X06pBPS4/qo3T4RjjmEDGAVwnIqn4at8qzpC9LkixNAM2VFjP4s+1e5Xt0wz4UwIoImPxfaOnaeMM3p+TRbTbRXyMm7SEGFLqxdA6PYHUejGkJ8bQIq0erRok0DKtHqn1osO+RuzIDul8cu2RvD8ni/9OWcbIp35i7OC2XD+sgz0WjiCLJ91GL93Gr0Mn0TopyelwnFSsqiXlv/ciEgVUMuhSeGnfMJGSMi8bdxXSskFkPPp/e1YWy7fm8eyFfa0ttIlogQwDczm+SdKbA3OBQcAvQLC6C1aWce1bAFdlH99G1fHAeIDMNqk665/HH1p0YcjtEs7ObMFxXRtz76eLeebbVUxZuIUHz+5Jv1YRMftDRNu86Ad6bHiDb5NPZcjRJzsdjtO+E5E7gHgRORa4Cvj4UE8qImnAW/iGz1oLnKOquyrZr9L2zyLyT+AKYLt/1ztU9TP/Z38DLgM8wHWqOiXQ+Npl+Ib6Wbl9T0QkgHnFZTw8dRkDWqdxfLfGTodjjKMC6a1wPdAfWKeqQ4E+/F4oBUMW0KLCenNgUzX2+bOSPCiJzJ5uVZFcL5oHz+7Fq5cNoMTj5ZznpvPUtJV4Kxud2oQFLSum7MNr2EYaXS6MjAGfD+J2fOXZAuAvwGfAnUE679eq2gH42r/+BxXaP58AdAVGiUjFngmPqGpv/1Ke/HUFzgO6ASOAp/3nCUj7hv4EMELaAT777Sp25JVwx0ldwv4pjzEHE0gCWKSqReAbFFpVlwKdghjLTKCDiLQRkRh8hdvkffaZDFwsPoOAnIO1/wNAvbDmhyCGGp6O6pDB59cfxYk9mvDglGWMfvFXtu+xIR/D0ZJ3/0WL0rUs6ns3jRpmOB2O41TVq6rPq+rZqnqW/30wvgGNBF72v38ZOK2Sffa2f1bVEqC8/fPBzvumqhar6hpgpf88AUnxN4GJhARw0+5Cnv9hNaf6O/EZE+kCSQCzRCQF+BCYKiIfUZXatypS1TLgGmAKsAR4W1UXicg4ERnn3+0zYDW+wu55fI9pDk7csOLLYIUa1pLionn8vN7cf0YPfl2zkxMf/4FZa3c6HZYJopx1C+iw9Dl+iD2aIadc7HQ44a5R+ZdU/2tlHUv217a53DUiMl9EJvrbYVflmL1EZKyIzBKRWdu3//mhTbsI6Qn80JRlKHDriGDWWxhTd1U5AVTV01V1t6r+E7gLeIHKv81Wm6p+pqodVbWdqt7n3/asqj7rf6+qerX/8x6qOqtKJ45NghVTqXQiXfMnIsJ5A1ry0TVHkBDj5vznZ/De7CynwzLB4PWy881x5Gkcjc97NGJ6ftYkEflKRBZWshysFm/vKSrZVl5YPYNvWJre+Dq7/a8Kx/xxo+p4Vc1U1cyMjD/X9rZv6EsAg1PhGZoWbszh/d82cukRbWieGv5tHY2pimqNWKyq36nqZP/jitAXVx9y1sPWhU5HUqd0blyfD68+gszWqdz0zjz+7/MleKxdYJ22+vNHaVO4kJ/a30SHNjb36b5EJCHQY1R1uKp2r2T5CNgqIk38524CbKvkFPtt26yqW1XVo6pefE89BhzsmEC1y0gkt6iMHXl1ozgPlKpy76eLSUuI4aqh7ZwOx5iQ4fyUFbUhLhkQWPKJ05HUOSn1Ynj50gFcMLAlz323mitfm02Rf45jU7cU7VhH45kP8Ku7N8PPvc7pcEKKiBwuIovxNT9BRHqJyNNBOPVkYLT//Wh8c6rva7/tn8uTR7/TgfJvsZOB80QkVkTa4Bue69fqBNihka8jyIpte6pzeMj7ask2pq/eyV+Hd6B+XOgP3G9MbYmMBNAVBa0OhyX79ikxVRHtdnHvad35x8ld+XLxVi6e+Cu5RaVOh2UCocqm165EVZGTHyMuJpAx4CPCI8DxQDaAqs4DBgfhvPcDx4rICnyzHJUP79JURD7zX6vS9s/+4/8rIgtEZD4wFPir/5hFwNv4Bsr/ArhaVav1zaxTY9/4j0s3h18C6PEqD3yxlLYZCZw3oKXT4RgTUgIZB1CAC4C2qvpvEWkJNFbVan3rrHVdToEvbocdKyG9vdPR1DkiwqVHtqFBYgw3vzOPc5+bzsuX9qdhUtzBDzaO2/zjq7Td/RMfNL6W0/v0djqckKSqG/YZGuSQq7pVNZtKppNT1U345jQvX/8MXye3ffe76ADnvg+471BjzEiMpUFCDEu35B7qqULOh79tZOW2PJ65oG9IzNFuTCgJ5DfiaeAwYJR/fQ++savqhi6n+F6XHvLYrhFtZO9mvDC6P+uy8znrmV/YsLPA6ZDMQXjzdlDvm78znw4MvuAOp8MJVRtE5HBARSRGRG7G/zg43IkInZsksXRLeNUAlpR5eeSr5fRolsyI7jboszH7CiQBHKiqVwNFAP7R7GNqJKqakNwcmvaFRR86HUmdN7hjBq9fMYicwlLOGz/dksAQt+7164j35rN58H9pUN96QO7HOHzzATfD18Git389InRpXJ9lW/aEVSevt2auJ2tXITcf38kGfTamEoEkgKX+keYVQEQyAG+NRFVTepwFm+fC9uVOR1Ln9W6RwqTLB5JXXGZJYAjbPe9T2mz6lI+TzuO4oUOdDidkqeoOVb1AVRupakNVvdD/+DYidG5Sn+IyL2uzw2PGpMISD49/s5IBbdIY3CHd6XCMCUmBtAR/HPgAaCgi9wFnEZypkmpP97Pgyzth/psw7B9OR1P7vF7YsRw2z/O97l4PhTt/nyYvKhbqNYD6TaFBe2jSCxp1B3flPee6N0tm0uUDuWDCDM4bP503rhgUEfOJ1hlFuXg/voEV2pw+F95jtSCVEJEn2M/4eQCqGhHdpTtX6AhSPj9wXfbyL2vZvqeYpy/oaz/3xuxHlRNAVZ0kIrPxNWgW4DRVrVttZJIaQduhMP8dGHonuCKgUXBpESz/AhZ9AGu+g0L/PPTihvrNIKEBxPgL/JIC2L0Bln4KZUW+bdH1oN0xvjaUHY+H+NQ/nL48CbzwhRmcN/4X3hx7mCWBIWLDO7fRrHQ73/R9kbMaN3A6nFBVtcHkw1z7hom4XcKSzbmc1LPJwQ8IYblFpTzz7SqGdsqgf+s0p8MxJmQFNBaEf/7fpTUUS+3odR68fwWs/wVaH+F0NDVnw0yY8xIsngzFuZDQEDqeAK2PhGZ9fTV8+6nZw+v1DZy96TdY+5MvIVz6iW84nQ7Hw2FXQasjwP/N+o81gZYEhoKC5d/RYtXrvB97KqeeVNUJKSKPqr588L3CX1y0m7bpCWHRE/j571eTU1jKTcfZlG/GHMhBE0AR2YPvEYnwx0clgm92tvo1FFvN6HySr8brt9fCLwFUhVXfwI+PwNofICbJV3PX82xoczS43FU7j8sFqa19S7fT4YT/+pLBxR/6/t2WfQpNesPh1/o+d7np1jSZ1y8fxPkTpnPhCzN4Z9xhNKpvQ8Q4orSQwveuZodm0Pbc+4mJioCa7kMkIh/z50fBOfhqCJ9T1aLaj6p2dWlSn9nrdjkdxiHZkVfMCz+u4aSeTejeLNnpcIwJaQf9y6CqSapav8Jr/YrrtRFkUMUkQM9zYNH7ULDT6WiCZ+2P8PxQeO0MyF4Jx/8HbloKpz/je4Rb1eSvMi4XNO8Hx90DNy6Gkx/1tRt87zIYfzSs+R6Ark3r8/IlA8jOK+aiF2awKz88p5YKdVsm302D4g180+FOerdr5nQ4dcVqIA/fdGvPA7nAVqCjfz3sdWlSn427C+v07+3T01ZRVOrhxmM7Oh2KMSGvylUDIvKyiKRUWE8VkYk1ElVNy7zM18Zt7utOR3Lodq+Ht0fDSydB/g445XG4fh4cdjXE1kBj7uh4yLwErv4VznwBCnPg5VPgjVGQvYpeLVKYMLo/a7MLGPPir+QVlwU/BrNfZRtmk7HgeSa7hnHW2Rc6HU5d0kdVz1fVj/3LhcAA/9BXfZ0Orjb0au6rMVuwMcfhSKpn4+5CXpu+jrP6NQ+LjizG1LRAng31VNXd5Sv+cQD7BD2i2tC4O7QYBLNe8LV3q4s8pfDdg/Bkf1g+BYbc4UvK+o329eataS6Xb1ida2bCsLthzQ/wzBHwy9Mc1iaVp8/vy8JNuVz+8kybO7i2lJWw+82/sEPrk3TqAyTG2nRvAcjwz24EgP99+fghdbdKLADd/I9M52ftdjaQanri6xUAXDesg8ORGFM3BJIAukRkbxdQEUkjwE4kIaX/ZbBzNaz62ulIArdlATx/DEy7FzqOgGtnwZDbIMaBjhfRcXDUjb5EsM1gmPI3eOlEhjfK4+FzejFjzU6ueX0OpZ46mmjXIbumPkh6/go+aHoTQ3vbH8EA3QT8KCLTRORb4AfgFhFJACKio0hyfDRt0xOYl1X3agBXb8/jndlZnD+wJc1TrQOaMVURSAL4P+BnEblHRP4N/Az8t2bCqgVdT/MNg/LjI05HUnWeMvj2fhg/BPZshnNehXNe9s1y4rT6TeD8t+C0Z2DrYnj2SEbyPf8e2Z2vlmzjlnfm4Q2jWQZCjW5bQuKMR/icwzlj1Finw6lz/HPxdgBu8C+dVPVTVc1X1UcdDK1W9WyezII6mAA+8tUKYqNcXD3U5nk3pqqqnACq6iv4Bn/eCmwHzlDVV2sqsBoXFQOHXQPrfoL1M5yO5uB2b/C18/v2/3w9b6/+Fbqe6nRUfyQCvc+Hq6dDs37w4Tgu2vogtw9vxYdzN3HPp4tRtSQw6Lwesl//C3s0loJj/kND631dXf2AbkBP4BwRudjheGpdj+YpbMktYltu3en0vHhTLh/P28SlR7QhI6kWmr8YEyYCGh9CVRep6pOq+oSqLq6poGpNv9EQnxb6tYBLPoZnj4Sti+CMCXDmBKgXwgOc1m8KF30IR90Ev73KX1b8hRv7RfHiT2t5+ttVTkcXdvK+fYz03fOYlHIlpx/Z2+lw6iQReRV4CDgS6O9fMh0NygHlHUHq0mPg/325jPpxUVwxuK3ToRhTp1RlHMAfVfXICuMB7v2IujgOYEUxCTDoSph2H2TN9g11EkpKi3xT18183jfu3lkToUE7p6OqGneUb7q9loch71/BtTljcXe4iwenQFpCDKMGtDz4OcxB6dZFxH7/H6Z6+3PC+dfjctm0V9WUCXTVCK+i7tY0GbdLmJ+1m2O7NnI6nIOavW4nXy/dxq0jOpEcv5+B7Y0xlarKOIBH+l/DYxzAfQ26EhIyYOpdvoGUQ8WOFTBhuC/5O+wauGxq3Un+KupwLIz9FklqwlVZt/Lvpr/w9w8W8MXCzU5HVveVlZA76RJ2azybjrqf9o2SnI6oLlsINA72SUUkTUSmisgK/2vqfvYbISLLRGSliNxeYftbIjLXv6wVkbn+7a1FpLDCZ88GI974GDcdGiYyd8PuYJyuRqkq//1iGemJsYw5vLXT4RhT59gUAbFJMOR2X1vA5V84HY3Pgnd9HT1yN8L5b8Px9/naLNZVqa3hsi+R9sO5eOcTPJUyib++MZufV+1wOrI6Lf/Le0jOXcbzKTdw4bAQq72ue9KBxSIyRUQmly9BOO/twNeq2gH42r/+ByLiBp4CTgC6AqNEpCuAqp6rqr1VtTfwHvB+hUNXlX+mquOCECsA/Vql8tv63XhCvNPWjyt3MGPNTq49pj31YurugBTGOKXKvzUiEgucCbSueJyq/jv4YdWyvqNh+jMw5Q5oO8Q32LETSovgi9th9ou+cQrPmgjJYTKTQ1x9GPUGfHU3J/z8BPXjd3DtK8rLYwfblE3VoOunE//rk7zrHcK5F/4Ftz36PVT/rKHzjgSG+N+/DHwL3LbPPgOAlaq6GkBE3vQft7edtYgIcA5wTA3F+XswbdKYNGM9Szbnhuzvpqry4JRlNEuJ57wBLZwOx5g6KZAawI/wFUplQH6Fpe5zR8NJ//ONC/jt/c7EkL3K98h39otwxA0w5pPwSf7Kudxw3L1w4kMcXvYrL7ru4bqJX7N2R3j8GNWa4jzy37ycjd4G5A+9x2Y9CAJV/a7igq+cOycIp26kqpv919gMNKxkn2bAhgrrWf5tFR0FbFXVFRW2tRGR30TkOxE5an8BiMhYEZklIrO2b99+0IAzW/s6mM1cG7pTZX6xcAvzs3K4fngHYqMOYZpLYyJYIPXmzVV1RI1F4rS2Q6DPhfDzE9DtNGhai5OcLHwfJl/n6zhx/tvQ8fjau7YTBlyBJGTQ470rmOC5k5smlPLMVSNt+JIqKvjkb9QryOK/6Q9w99E9nA4nbIhIb+B8fInfGnyPXKty3FdU3n7w71W9dCXb9n3+Ogp4o8L6ZqClqmaLSD/gQxHppqq5fzqR6nhgPEBmZuZBn+s2S4mnWUo8M9fu5JIj2lTxFmpPmcfLg18uo0PDRM7sGwJjoBpTRwVSA/iziIT3X5vj7oXEhvDOJVC4u+avV1oIn94E714CDbvAX34I/+SvXLfTkIs/oFXMHp4qvJ27nn+HnMJSp6MKebp8CvUWvMKL3pO59PwL7dHvIRKRjiLyDxFZAjyJryZOVHWoqj5ZlXOo6nBV7V7J8hGwVUSa+K/VBNhWySmygIrPMZsDmyrEGAWcAbxV4ZrFqprtfz8bWAV0DODWD6h/61Rmrt0VkuN2vjM7i9Xb87nl+E7282/MIThoAigiC0RkPr7xseb4e6rNr7A9fMSnwtkvQc4G+PCqmp0neOMceO5omDkBDr8WLvkMUiKsLUvrI3Ff9gWp9aJ5MPdWHnr+RZs3+EByN1H87l9Y4m1BzLF30To9wemIwsFSYBhwiqoeqapPAMH8IZwMjPa/H42vKc2+ZgIdRKSNiMQA5/mPKzccWKqqWeUbRCTD33kEEWmLbxaT1cEKun+bNLbvKWZddkGwThkUhSUeHv1qOf1apdaJYWqMCWVVqQE8GTgFXw+19sBx/vXy7eGl5SBfTeCyT32dQoL9DdhT6mtnOGE4FO+Biz7wXc8doWNYNepG7F++Ruo35u/Zd/D8hKcos3mD/8zrofDNS/EWF/BC439wwRFBq+yJdGcCW4BpIvK8iAyj8key1XU/cKyIrACO9a8jIk1F5DMAVS0DrgGmAEuAt1V1UYVznMcfH/8CDAbmi8g84F1gnKoGrdFef387wF9DrB3gSz+vZWtuMbeN6IyvX4wxproO2gZQVdfB3l5oFwBtVfXfItISX7uXdTUbogMGjoNd62DGMxBTD465yzfN2aFa+xN8fitsXQg9z4MTHoD4lEM/b12X0oKkcV+x47lTuHLL3bwzsZDzLr/VCvgKyqbdT/ymX7jLdQ23XHiqDfgcJKr6AfCBiCQApwF/BRqJyDPAB6r65SGePxtfDeO+2zcBJ1ZY/wz4bD/nGFPJtveoYhvF6mifkUh6Ygw/rdzBOZmh8WQip6CUZ75dyTGdGzKgTQjPhGRMHRFIG8CngcPwNUYG2INv7KrwIwIj/s83PMwP/4MPxvmGaKmu3RvgnTHw0olQlAvnToIznrPkr6KEBqRfPYVNKf0YtfE/fP3i3U5HFDrWfI/7hwd5z3MUg8++jkbWWSboVDVfVSep6sn42uDNpZIx+yKFyyUc2T6dH1bswBsi4wE+/d1K9hSXccvxnZwOxZiwEEgCOFBVrwaKAFR1F1CHRyc+CBE45TEY+neY/yY8fwxs+DWwc+zeAJ/fBk9mwrIvYMgdcM2v0OXkmom5rotNosU1n7AweSjD1z/GbxNvCK3ZWZywZwvFb1/Gam9jFvf+h7V7qgWqulNVn1PVGh9zL5QN7pjBzvwSFm/+U8fiWrc5p5CXflrLab2b0aVJ3Z+AyphQEEgCWOpvdKzga4QMBKWxVgDTJU0UkW0isjAY161CYHD0rTDqLSjcBS8cB29eAKu/9bXlq0zBTpj/Dkw6Bx7r6evk0f0sX+I35DbnBpmuIyQ6ji7XvssPyafQZ/2LrH7xcvBGaMeQshJK3rgQT2EuD9T/G7ecarN9mNpzVIcMAL5bfvCxA2vaY1+twKvKjcda21djgiWQcQAfBz4AGorIfcBZwJ1BiqN8uqT7/fNg3s6fR8sHeAnfUA2vBOm6VdNpBLQ+An58FGZNhKWfQEwiNOkNSY3BFQVFObBjuW8waRSSmsCRN0K/MZHXu/cQuaOiGHDNS3z4+DWctv4Ntk7cQ6Mxr0JUrNOh1SrPZ7cQs2kmt3pu4KYLzyAu2ga8NbUnIymWrk3q8/3y7Vw9tL1jcazclsfbszZw8WGtaZFWz7E4jAk3B00AReRJ4HVVnSQis/E1aBbgNFVdEqQ4qjJdEqr6vYi0DtI1AxObBMPugsE3w/IpsOZ72LoINs4C9UJMEjTqCr3Og3bDfANJu2yq5eqKjY5i+DVPMuHxRC7Pep6cF04necxbvv8PkWD2S7jnvMQzZacw9KyxdGocIfdtQsrgjhlM+GE1ecVlJMY6M9/uvZ8uJiEmimuOcS4JNSYcVeU3egXwP/8gpm8Bb6jq3CDH8YfpkkSksumSAiIiY4GxAC1btjzU0/0uOt43U0i304J3TlOpxNgoTr/yPv7viQRu2fw4hRNOJH7MB5CQ7nRoNWv9DDyf3sxPnh5szbyFK3uH2ZSAps4Y0imDZ79bxffLt3Nijya1fv1pS7fx7bLt/P3ELqQnRtYTAGNq2kGrqFT1MVU9DDga2Am8KCJL/KPnV7lBhoh8JSILK1lGHkL8B4p7vKpmqmpmRkZGTVzC1IIGibFcNO42bou6Hdm+lNIJx/k614Sr7FV4Xj+XjZ40xje8kztODu/Jd0xo6986jQYJMXy2YHOtX7vU4+WeTxfTJj2B0Ye3rvXrGxPuqvyMUlXXqeoDqtoH33yZp+MbtLSqxx/qdEkmQjVPrcdfrriKcdxJ8a7NeCYcB9uXOR1W8OXvwPPqGewp8nCd+07+e9HRxERZMwLjHLdLOL57Y75Zuq3WZ+l55Zd1rN6ez50ndbHfA2NqQJV/q0QkWkROEZFJwOfAcnyj6AdDVaZLMhGsY6Mkrr3kYs733E1OfiHeiSMga7bTYQVPSQHe18/Bs3sTV5Tdwl2jT6FpivUYN847sXsTCko8tdobODuvmEe/Ws7gjhkc0/mQWwQZYypRlbmAjxWRifgmLB+Lb7T6dqp6rqp+GKQ4Djpdkn/9DeAXoJOIZInIZUG6vqkD+rVK5daLz+Ls0n+ypTgGfflkWPWN02EdOk8p+t6lsHEO15ZczcVnn0W/VpWOhGRMrRvYNo3UetF8XouPgf83dTkFJR7uOqmLzQhkTA2pSg3gHfiSri6qeop/tPz8YAahqtmqOkxVO/hfd/q3b1LVitMljVLVJqoararNVfWFYMZhQt+RHdK5Z8zJnFv6L1Z5GqGTzoHfJjkdVvV5SuG9y5Bln3N36Wi6D7uAU3o1dToqY/aKdrs4rmtjpi7eSn5xWY1fb9banbw+Yz2jD2tNh0bW+92YmlKVTiBDVfX5YE40bsyhOLx9Og9dciwXlN3FbOkKH10FU/5e9waM9pTB+1fA4o+4p/RC8nteYkNdmJB0VmZz8ks8fDq/ZmsBi0o93PbefJqlxHPTcTboszE1yVrWmjppYNsGPHXpUC4vu513XCfAL0/CG6N8cy3XBZ4y+GAsLPqA+0rPZ13HS3jgrJ72uMuEpMxWqbRvmMgbM9fX6HWemraSVdvz+c8ZPUhwaNxBYyKFJYCmzspsncbrfzmS/7ov514uR1d+Bc8P9Q3QHcpK8uHti2Hhe9xfNoqlbcfw5Pl9iHbbr6MJTSLCef1b8Nv63SzdUjNfspZuyeWZb1dxRp9mHN3Rhu4ypqbZXxxTp3VtWp/3rzycrxJO5uKyv1OcnwPPHwO/veZ0aJXL2wYvnYwu+5x/lY1hTvPRjL8o06Z5MyHvjL7NiXG7eH1G8GsBPV7ltvcWkBwfzV0ndw36+Y0xf2YJoKnzWqTV490rDyen0UCOzPk3WYk94KOr4YMrQ+uR8PblMGEYpVsXM7b0r8xvdi4vjMkkPsaSPxP60hJiOLV3U96auYFte4qCeu6np61k3obd3H1qN1ITYoJ6bmNM5SwBNGEhPTGWt8YexmE9uzB4y/V8ljYanf8mPHN4aAwVM/8ddMIw8vPzOKPgTrTjiUy6fCBJcdFOR2ZqkIikichUEVnhf610fB8RmSgi20RkYVWPF5G/ichKEVkmIsfX9L0AXD20PaUeLxN+WBO0c85au5NHv17ByN5NOaVn7U83Z0yksgTQhI34GDePndebW0Z05erNx3Nj4n8pccXCq6fD5GuhKKf2gyreAx+Mg/cvZ52rJcftuZtumUfz7IV97bFvZLgd+FpVOwBf+9cr8xIwoqrHi0hX4Dygm/+4p0Wkxn+g2qQncGqvprz6yzqy84oP+Xw780u4/s25NE2J497TulsnKGNqkSWAJqyICFcOaccLozP5Jq8V/XfczaK2l6K/vQaP94WZE3xj79WGtT/Bc4PR+W8xKW4Uw3bdxpnDDuf/zuhBlHX4iBQjgZf9718GTqtsJ1X9Ht9c61U9fiTwpqoWq+oaYCUwIDghH9g1x7SnuMzDI18tP6TzlHq8XDVpNtvzinnq/L5WG25MLbO/QiYsHdO5EVNuGEz3Vg05afFw7mnyFKVpHeHTm+Dpw2DJJ+D11szFd6+H98fCSydSUFTEaO/dPFhyBuNHD+TGYztaLUdkaaSqmwH8r4HOa7a/45sBGyrsl+Xf9iciMlZEZonIrO3bD306t/YNkxh9eGsmzVjP7HW7qnUOVeXuyYuYvnon95/Rg57NUw45LmNMYCwBNGGrcXIcr146kDtP6sJr61Lpm3U9X/Z8FAV46wJ4agD8+rzvMW0wZK/yJZhP9EMXfciXDS6i7877yGvUn0+vO4phXRoF5zompIjIVyKysJJlZE1etpJtWtmOqjpeVTNVNTMjIzjDq9x0XCea1I/jjvcXUFwW+ADsD325jNdnrGfc0e04o2/zoMRkjAmMjbRpwprLJVx+VFuGdGrIvz9ZzNhfPXRocD+PDFxDt6w3kM9uhq//Dd3PgK6nQavDISq26hco3A0rpsL8N2Hl16grihVNTua6TcexcnMKVx7TjuuGdbAx/sKYqg7f32cislVEmqjqZhFpAmwL8PT7Oz4LaFFhv+bApgDPXW2JsVHcd3oPLnlpJre9O59Hzu1dpZptVeV/Xy7nqWmrGDWgJbeN6FQL0RpjKmMJoIkI7Rsm8vIl/Zm2bBv3frKEk79rSqdG/+Tmw3M5Jvcj3PPfgdkvQVQ8tBwITXpBeidIbgZxyeCOhbIiKNoNuzfAtiWwcbZvUQ9avzkL243lH5sG8tuqOA5v14BPT+lGp8Y2l2mEmwyMBu73v34UpOMnA6+LyMNAU6AD8GswAq6qoZ0bcsvxnXhwyjKapcZz83GdDpgEFpV6uOODBbw/ZyPnZrawTh/GOMwSQBMxRIRjOjfiyPYZfDR3Iy/8uIYrvhEaJJzDWb2u5OzUlbTdMxPX+ukw/RnwlOz/ZNH10MY92dzjSj4v6s4Ty1PZvc1DrxYpvDiyA0M6ZdgfNwO+xO1tEbkMWA+cDSAiTYEJqnqif/0NYAiQLiJZwN2q+sL+jlfVRSLyNrAYKAOuVtVanwz7qiHtWJ9dwFPTVrF+ZyH372cKt5lrd3Lbu/NZvSOfG4/tyLXHtLffD2McJqqVNhsJK5mZmTpr1iynwzAhRlX5ZXU2L/20lm+XbafE4yUpLooBrdPo3jieLvVyaerKpp4W4vYUU6gx7CiLZVlRKjN2xDJrQy67C0qJcbs4vntjRg1owWFtG9gftlokIrNVNdPpOOqKmigLVZVnvlvFQ1OWkRwfzagBLenTMpWEGDcrt+fxybzN/Lp2J81S4vnvWT05on16UK9vjKleWWg1gCZiiQiHt0vn8Hbp5BaVMm3pNn5Zlc3sdbv4dvl2PF7F108qwb+UH5dHm3Tl2C6NGNwxgyGdMmwICxOxRISrhrRnYJsGPPfdKp75bhUV6xVapMVz50ldOG9ASxIrqR00xjjDfhuNAerHRTOydzNG9vaNpFFU6mFzThHbcosoLPXgVSUxNpq0hBhapMUTG2WDOBtTUb9WqYy/OJNd+SWs31nAnqIy2jVMoHH9OKsVNyYEWQJoTCXiot20SU+gTXrCwXc2xuyVmhBj8/kaUwfY2BTGGGOMMRHGEkBjjDHGmAhjCaAxxhhjTISJiGFgRGQPsMzpOA5ROrDD6SCCIBzuIxzuAcLjPjqpqo22XUVWFoaUcLiPcLgHCI/7CLgsjJROIMvq+lhhIjKrrt8DhMd9hMM9QHjch4jYAJ+BsbIwRITDfYTDPUB43Ed1ykJ7BGyMMcYYE2EsATTGGGOMiTCRkgCOdzqAIAiHe4DwuI9wuAcIj/sIh3uoTeHw7xUO9wDhcR/hcA8QHvcR8D1ERCcQY4wxxhjzu0ipATTGGGOMMX6WABpjjDHGRJiwTgBFZISILBORlSJyu9PxVIeItBCRaSKyREQWicj1TsdUXSLiFpHfROQTp2OpLhFJEZF3RWSp///JYU7HFCgR+av/Z2mhiLwhInFOx1QVIjJRRLaJyMIK29JEZKqIrPC/pjoZY6iysjC0WFkYGiK9LAzbBFBE3MBTwAlAV2CUiHR1NqpqKQNuUtUuwCDg6jp6HwDXA0ucDuIQPQZ8oaqdgV7UsfsRkWbAdUCmqnYH3MB5zkZVZS8BI/bZdjvwtap2AL72r5sKrCwMSVYWOszKwjBOAIEBwEpVXa2qJcCbwEiHYwqYqm5W1Tn+93vw/ZI1czaqwIlIc+AkYILTsVSXiNQHBgMvAKhqiarudjSo6okC4kUkCqgHbHI4nipR1e+BnftsHgm87H//MnBabcZUR1hZGEKsLAwpEV0WhnMC2AzYUGE9izpYWFQkIq2BPsAMh0OpjkeBWwGvw3EcirbAduBF/+ObCSKS4HRQgVDVjcBDwHpgM5Cjql86G9UhaaSqm8GXIAANHY4nFFlZGFoexcpCx1lZGN4JoFSyrc6OeSMiicB7wA2qmut0PIEQkZOBbao62+lYDlEU0Bd4RlX7APnUsUeO/nYhI4E2QFMgQUQudDYqU8OsLAwRVhaGDisLwzsBzAJaVFhvTh2p3t2XiETjK/Amqer7TsdTDUcAp4rIWnyPn44RkdecDalasoAsVS2vdXgXXyFYlwwH1qjqdlUtBd4HDnc4pkOxVUSaAPhftzkcTyiysjB0WFkYOiK+LAznBHAm0EFE2ohIDL7GnZMdjilgIiL42lksUdWHnY6nOlT1b6raXFVb4/v/8I2q1rlvWqq6BdggIp38m4YBix0MqTrWA4NEpJ7/Z2sYdazx9j4mA6P970cDHzkYS6iysjBEWFkYUiK+LIyq0XAcpKplInINMAVf756JqrrI4bCq4wjgImCBiMz1b7tDVT9zLqSIdi0wyf+HdDVwicPxBERVZ4jIu8AcfL0qf6OOTIMkIm8AQ4B0EckC7gbuB94WkcvwFehnOxdhaLKy0NQQKwsdEqyy0KaCM8YYY4yJMOH8CNgYY4wxxlTCEkBjjDHGmAhjCaAxxhhjTISxBNAYY4wxJsJYAmiMMcYYE2EsATTGGGOMiTCWABpjjDHGRBhLACOYiKiI/K/C+s0i8s9ajiGvwvufg3C+f4rIzZVsTxGRq4J5rUMlIs1F5Nx9tj0nIkeIyBARedWp2IyJJFYWOsvKQmdYAhjZioEzRCQ90APFJ6g/P6pak/MwpgB7C70avlZVDePP82cOBKYDvfGNTG+MqXlWFjrLykIHWAIY2crwTX3z130/EJEbRWShf7nBv621iCwRkafxTZ9zlIgsFZEJ/v0michwEflJRFaIyIAK5/tQRGaLyCIRGVtZMOXfgEVknIjM9S9rRGSaf/uFIvKrf/tzIuL2b/+7iCwTka+ATpWdG980Oe38xz5Y4VqtA7iHSq9f4fN+5bH617uLyC/7udcjgYeBs/znayMiXYDlquoBegHNRGSGiKwWkSH7uS9jzKGzstDKwsijqrZE6ALkAfWBtUAycDPwT6AfsABIABKBRUAfoDXgBQb5j2+Nr+Dsge/LxGxgIiDASODDCtdK87/GAwuBBuUxVIxnn/iigR+AU4AuwMdAtP+zp4GLK8Raz38vK4GbK7nX1sDCfa9V1XvY3/X3uUY9YGOF9feB4Qf49/8C6F5h/UbgUv/734B/+t8fB/zg9M+LLbaE62JloZWFkbhEYSKaquaKyCvAdUChf/ORwAeqmg8gIu8DRwGTgXWqOr3CKdao6gL/fouAr1VVRWQBvgKl3HUicrr/fQugA5B9kPAeA75R1Y/FN5l9P2CmiICv8NwGpPljLfDHMDnQf4Mq3sOw/Vx/L1UtEJEiEUkB2gKpqvqViCTgKyRLgG9VdZL/kE7AsgqnOB64RESigAbAf/zb5wIBP5oyxlSdlYVVvgcrC8OEJYAG4FF8jzFe9K/LAfbN32e9uMJ7b4V1L/6fL3+V/XDgMH/B8C0Qd6CARGQM0Aq4pkJML6vq3/bZ7wZAD3SuKjjoPezv+pVYDHQG7gLu9G87A3jXX3i/BUwSkQZAjqqW+u+jHpCiqptEpCewUlVL/Mf3BeZV//aMMVX0KFYWlrOyMMxZG0CDqu4E3gYu82/6HjhNROr5v7Gdju/xQ3UlA7v8BV5nYNCBdhaRfvgewVyoql7/5q/xtRFp6N8nTURa+WM9XUTiRSQJ3yOSyuwBkg7hHvZ3/X0tAi4BRFV/8m9rDmzwv/f4X9sAmyocNxQobzPTC2gjIrEikgjcje8PkzGmBllZWCVWFoYJqwE05f6H/xumqs4RkZeAX/2fTVDV30SkdTXP/QUwTkTm46vmn36Q/a/B9zhjmv8RwyxVvVxE7gS+FF+Pu1LgalWd7v8mORdYx34KZ1XN9jdmXgh8HugNqOriyq7vv2ZFi4CXgf4VtmXhK/jm8vuXrqVAuj+escAJwLv+z3oBk4Cf8T1euWefR03GmJpjZeEBWFkYPkT1UGuMjTEH4q85eBIoAn6s0O6l4j5zgIHlj0GMMSbcWFkYWiwBNMYYY4yJMNYG0BhjjDEmwlgCaIwxxhgTYSwBNMYYY4yJMJYAGmOMMcZEGEsAjTHGGGMijCWAxhhjjDERxhJAY4wxxpgIYwmgMcYYY0yE+X9K14YU9/+SPAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 648x324 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Convert the curvy trajectory into normalized coordinates\n",
    "x_ref = x_curvy[0] / wheelbase\n",
    "y_ref = x_curvy[1] / wheelbase\n",
    "theta_ref = x_curvy[2]\n",
    "tau = v0 * T_curvy / b\n",
    "\n",
    "# Simulate the estimator, with a small initial error in y position\n",
    "t, y_est, x_est = ct.forced_response(est, tau, [delta_curvy, y_ref], [0.5, 0], return_x=True)\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the actual and estimated states\n",
    "ax = plt.subplot(2, 2, 1)\n",
    "plt.plot(t, y_ref)\n",
    "plt.plot(t, x_est[0])\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.legend(['actual', 'estimated'])\n",
    "plt.ylabel('Lateral position $y/b$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 2)\n",
    "plt.plot(t, x_est[0] - y_ref)\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.ylabel('Lateral error')\n",
    "\n",
    "ax = plt.subplot(2, 2, 3)\n",
    "plt.plot(t, theta_ref)\n",
    "plt.plot(t, x_est[1])\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Vehicle angle $\\\\theta$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 4)\n",
    "plt.plot(t, x_est[1] - theta_ref)\n",
    "ax.set(xlim=[0, 10])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Angle error')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Output Feedback Controller (Example 8.4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [[0.49   0.7448]]\n",
      "kf =  0.4899999999999182\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x324 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the feedback gains\n",
    "# K, kf, clsys = normalized_place(1, 0.707)     # Gains from MATLAB\n",
    "# K, kf, clsys = normalized_place(0.07, 0.707)  # Original gains\n",
    "K, kf, clsys = normalized_place(0.7, 0.707)       # Final gains\n",
    "\n",
    "# Print out the gains\n",
    "print(\"K = \", K)\n",
    "print(\"kf = \", kf)\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "clsys = ct.StateSpace(\n",
    "    np.block([[A, -B@K], [L@C, A - B@K - L@C]]),\n",
    "    np.block([[B], [B]]) * kf, \n",
    "    np.block([[C, np.zeros(C.shape)], [np.zeros(C.shape), C]]), \n",
    "    np.zeros((2,1)))\n",
    "\n",
    "# Simulate the system\n",
    "t, y, x = ct.forced_response(clsys, tau, y_ref, [0.4, 0, 0.0, 0], return_x=True)\n",
    "\n",
    "# Calcaluate the input used to generate the control response\n",
    "u_sfb = kf * y_ref - K @ x[0:2]\n",
    "u_ofb = kf * y_ref - K @ x[2:4]\n",
    "\n",
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "# Plot the actual and estimated states\n",
    "ax = plt.subplot(1, 2, 1)\n",
    "plt.plot(t, x[0])\n",
    "plt.plot(t, x[2])\n",
    "plt.plot(t, y_ref, 'k-.')\n",
    "ax.set(xlim=[0, 30])\n",
    "plt.legend(['state feedback', 'output feedback', 'reference'])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Lateral position $y/b$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 2)\n",
    "plt.plot(t, x[1])\n",
    "plt.plot(t, x[3])\n",
    "plt.plot(t, theta_ref, 'k-.')\n",
    "ax.set(xlim=[0, 15])\n",
    "plt.ylabel('Vehicle angle $\\\\theta$')\n",
    "\n",
    "ax = plt.subplot(2, 2, 4)\n",
    "plt.plot(t, u_sfb[0])\n",
    "plt.plot(t, u_ofb[0])\n",
    "plt.plot(t, delta_curvy, 'k-.')\n",
    "ax.set(xlim=[0, 15])\n",
    "plt.xlabel('Normalized time $v_0 t / b$')\n",
    "plt.ylabel('Steering angle $\\\\delta$')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Trajectory Generation (Example 8.8)\n",
    "\n",
    "To illustrate how we can use a two degree-of-freedom design to improve the performance of the system, consider the problem of steering a car to change lanes on a road.  We use the non-normalized form of the dynamics, which were derived in Example 3.11."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import control.flatsys as fs\n",
    "\n",
    "# Function to take states, inputs and return the flat flag\n",
    "def vehicle_flat_forward(x, u, params={}):\n",
    "    # Get the parameter values\n",
    "    b = params.get('wheelbase', 3.)\n",
    "    \n",
    "    # Create a list of arrays to store the flat output and its derivatives\n",
    "    zflag = [np.zeros(3), np.zeros(3)]\n",
    "    \n",
    "    # Flat output is the x, y position of the rear wheels\n",
    "    zflag[0][0] = x[0]\n",
    "    zflag[1][0] = x[1]\n",
    "    \n",
    "    # First derivatives of the flat output\n",
    "    zflag[0][1] = u[0] * np.cos(x[2])  # dx/dt\n",
    "    zflag[1][1] = u[0] * np.sin(x[2])  # dy/dt\n",
    "    \n",
    "    # First derivative of the angle\n",
    "    thdot = (u[0]/b) * np.tan(u[1])\n",
    "\n",
    "    # Second derivatives of the flat output (setting vdot = 0)\n",
    "    zflag[0][2] = -u[0] * thdot * np.sin(x[2])\n",
    "    zflag[1][2] =  u[0] * thdot * np.cos(x[2])\n",
    "    \n",
    "    return zflag\n",
    "\n",
    "# Function to take the flat flag and return states, inputs\n",
    "def vehicle_flat_reverse(zflag, params={}):\n",
    "    # Get the parameter values\n",
    "    b = params.get('wheelbase', 3.)  \n",
    "\n",
    "    # Create a vector to store the state and inputs\n",
    "    x = np.zeros(3)\n",
    "    u = np.zeros(2)\n",
    "    \n",
    "    # Given the flat variables, solve for the state\n",
    "    x[0] = zflag[0][0]  # x position\n",
    "    x[1] = zflag[1][0]  # y position\n",
    "    x[2] = np.arctan2(zflag[1][1], zflag[0][1])  # tan(theta) = ydot/xdot\n",
    "    \n",
    "    # And next solve for the inputs\n",
    "    u[0] = zflag[0][1] * np.cos(x[2]) + zflag[1][1] * np.sin(x[2])\n",
    "    thdot_v = zflag[1][2] * np.cos(x[2]) - zflag[0][2] * np.sin(x[2])\n",
    "    u[1] = np.arctan2(thdot_v, u[0]**2 / b)\n",
    "    \n",
    "    return x, u\n",
    "\n",
    "vehicle_flat = fs.FlatSystem(vehicle_flat_forward, vehicle_flat_reverse, inputs=2, states=3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Utility function to plot lane change trajectory\n",
    "def plot_vehicle_lanechange(traj):\n",
    "    # Create the trajectory\n",
    "    t = np.linspace(0, Tf, 100)\n",
    "    x, u = traj.eval(t)\n",
    "\n",
    "    # Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "    plt.figure(figsize=[9, 4.5])\n",
    "\n",
    "    # Plot the trajectory in xy coordinate\n",
    "    plt.subplot(1, 4, 2)\n",
    "    plt.plot(x[1], x[0])\n",
    "    plt.xlabel('y [m]')\n",
    "    plt.ylabel('x [m]')\n",
    "\n",
    "    # Add lane lines and scale the axis\n",
    "    plt.plot([-4, -4], [0, x[0, -1]], 'k-', linewidth=1)\n",
    "    plt.plot([0, 0], [0, x[0, -1]], 'k--', linewidth=1)\n",
    "    plt.plot([4, 4], [0, x[0, -1]], 'k-', linewidth=1)\n",
    "    plt.axis([-10, 10, -5, x[0, -1] + 5])\n",
    "\n",
    "    # Time traces of the state and input\n",
    "    plt.subplot(2, 4, 3)\n",
    "    plt.plot(t, x[1])\n",
    "    plt.ylabel('y [m]')\n",
    "\n",
    "    plt.subplot(2, 4, 4)\n",
    "    plt.plot(t, x[2])\n",
    "    plt.ylabel('theta [rad]')\n",
    "\n",
    "    plt.subplot(2, 4, 7)\n",
    "    plt.plot(t, u[0])\n",
    "    plt.xlabel('Time t [sec]')\n",
    "    plt.ylabel('v [m/s]')\n",
    "    # plt.axis([0, t[-1], u0[0] - 1, uf[0] + 1])\n",
    "\n",
    "    plt.subplot(2, 4, 8)\n",
    "    plt.plot(t, u[1]);\n",
    "    plt.xlabel('Time t [sec]')\n",
    "    plt.ylabel('$\\delta$ [rad]')\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To find a trajectory from an initial state $x_0$ to a final state $x_\\text{f}$ in time $T_\\text{f}$ we solve a point-to-point trajectory generation problem.  We also set the initial and final inputs, which sets the vehicle velocity $v$ and steering wheel angle $\\delta$ at the endpoints."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x324 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the endpoints of the trajectory \n",
    "x0 = [0., 2., 0.]; u0 = [15, 0.]\n",
    "xf = [75, -2., 0.]; uf = [15, 0.]\n",
    "Tf = xf[0] / uf[0]\n",
    "\n",
    "# Define a set of basis functions to use for the trajectories\n",
    "poly = fs.PolyFamily(8)\n",
    "\n",
    "# Find a trajectory between the initial condition and the final condition\n",
    "traj1 = fs.point_to_point(vehicle_flat, Tf, x0, u0, xf, uf, basis=poly)    \n",
    "plot_vehicle_lanechange(traj1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Change of basis function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x324 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "bezier = fs.BezierFamily(8)\n",
    "traj2 = fs.point_to_point(vehicle_flat, Tf, x0, u0, xf, uf, basis=bezier)\n",
    "plot_vehicle_lanechange(traj2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  Added cost function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 648x324 with 5 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "timepts = np.linspace(0, Tf, 12)\n",
    "poly = fs.PolyFamily(8)\n",
    "traj_cost = opt.quadratic_cost(\n",
    "    vehicle_flat, np.diag([0, 0.1, 0]), np.diag([0.1, 10]), x0=xf, u0=uf)\n",
    "constraints = [\n",
    "     opt.input_range_constraint(vehicle_flat, [8, -0.1], [12, 0.1]) ]\n",
    "\n",
    "traj3 = fs.point_to_point(\n",
    "     vehicle_flat, timepts, x0, u0, xf, uf, cost=traj_cost, basis=poly\n",
    ")\n",
    "plot_vehicle_lanechange(traj3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vehicle transfer functions for forward and reverse driving (Example 10.11)\n",
    "\n",
    "The vehicle steering model has different properties depending on whether we are driving forward or in reverse.  The figures below show step responses from steering angle to lateral translation for a the linearized model when driving forward (dashed) and reverse (solid). In this simulation we have added an extra pole with the time constant $T=0.1$ to approximately account for the dynamics in the steering system.\n",
    "\n",
    "With rear-wheel steering the center of mass first moves in the wrong direction and the overall response with rear-wheel steering is significantly delayed compared with that for front-wheel steering. (b) Frequency response for driving forward (dashed) and reverse (solid). Notice that the gain curves are identical, but the phase curve for driving in reverse has non-minimum phase."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Forward TF =  \n",
      "          s + 1.333\n",
      "-----------------------------\n",
      "s^2 + 7.828e-16 s - 1.848e-16\n",
      "\n",
      "Reverse TF =  \n",
      "          -s + 1.333\n",
      "-----------------------------\n",
      "s^2 - 7.828e-16 s - 1.848e-16\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Magnitude of the steering input (half maximum)\n",
    "Msteer = vehicle_params['maxsteer'] / 2\n",
    "\n",
    "# Create a linearized model of the system going forward at 2 m/s\n",
    "forward_lateral = ct.linearize(lateral, [0, 0], [0], params={'velocity': 2})\n",
    "forward_tf = ct.ss2tf(forward_lateral)[0, 0]\n",
    "print(\"Forward TF = \", forward_tf)\n",
    "\n",
    "# Create a linearized model of the system going in reverise at 1 m/s\n",
    "reverse_lateral = ct.linearize(lateral, [0, 0], [0], params={'velocity': -2})\n",
    "reverse_tf = ct.ss2tf(reverse_lateral)[0, 0]\n",
    "print(\"Reverse TF = \", reverse_tf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Configure matplotlib plots to be a bit bigger and optimize layout\n",
    "plt.figure()\n",
    "\n",
    "# Forward motion\n",
    "t, y = ct.step_response(forward_tf * Msteer, np.linspace(0, 4, 500))\n",
    "plt.plot(t, y, 'b--')\n",
    "\n",
    "# Reverse motion\n",
    "t, y = ct.step_response(reverse_tf * Msteer, np.linspace(0, 4, 500))\n",
    "plt.plot(t, y, 'b-')\n",
    "\n",
    "# Add labels and reference lines\n",
    "plt.axis([0, 4, -0.5, 2.5])\n",
    "plt.legend(['forward', 'reverse'], loc='upper left')\n",
    "plt.xlabel('Time $t$ [s]')\n",
    "plt.ylabel('Lateral position [m]')\n",
    "plt.plot([0, 4], [0, 0], 'k-', linewidth=1)\n",
    "\n",
    "# Plot the Bode plots\n",
    "plt.figure()\n",
    "plt.subplot(1, 2, 2)\n",
    "ct.bode_plot(forward_tf[0, 0], np.logspace(-1, 1, 100), color='b', linestyle='--')\n",
    "ct.bode_plot(reverse_tf[0, 0], np.logspace(-1, 1, 100), color='b', linestyle='-')\n",
    "plt.legend(('forward', 'reverse'));\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feedforward Compensation (Example 12.6)\n",
    "\n",
    "For a lane transfer system we would like to have a nice response without overshoot, and we therefore consider the use of feedforward compensation to provide a reference trajectory for the closed loop system.  We choose the desired response as $F_\\text{m}(s) = a^22/(s + a)^2$, where the response speed or aggressiveness of the steering is governed by the parameter $a$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAagAAAEZCAYAAADCJLEQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nO3deZgU5bX48e+Znn1lVhiGZdgRFwRGUNHEPZiIaGLcbtwjGvVGs5tVvMnN9WduTG42BeOamBjjEtG479GIwKAoyL7JwMCwz8DsM+f3R9VgM3TP2t1VPXM+z1NPd1VXd52C7jn1LvW+oqoYY4wxfpPgdQDGGGNMKJagjDHG+JIlKGOMMb5kCcoYY4wvWYIyxhjjS5agjDHG+JIlKGOMMb6U6HUAxsQzERkETAUUWKSq2zwOyZg+w0pQxvSQiHwVWAh8EbgAWCAiV3sblTF9h9hIEsb0jIisAk5U1V3uej7wb1Ud521kxvQNVoIypucqgJqg9Rpgs0exGNPnWBuUMd0kIt90n24B3hORp3HaoGbhVPkZYyLAEpQx3ZflPq5zlzZPexCLMX2WJShjuq8JeF5V3/c6EGP6MktQxnTfeuBmEZkILAWeB15S1T3ehmVM32K9+IzpBRGZBMwAzgICwCvAC6pqbVHG9FJME1RBQYGWlpbG7HjGdEV5eflOVS3s7eeISDZwJvA5VZ3d+8giy35/xq/C/QZjWsVXWlrK4sWLY3lIYzolIpt6+L7FwAPAX1R1j6pWA0+4S29jmgH8H06p7I+qeke710/B6ZSxwd30pKr+V0efab8/41fhfoN2H5QxPXcxMBhYJCKPisjnRER6+6EiEgB+D5wNTAAuEZEJIXb9l6oe6y4dJidj4pElKGN6SFXXquoPgbHAX4D7gU9E5HYRyevFR08F1qrqelVtBB7Fuccqav626BMeL6/gzdU72LW/IZqHMqbLrBefMb0gIscAVwGfx6naewQ4CXgNOLaHH1vCoSNSVADTQux3gogsBbYC31bV5SHimw3MBhg2bFjYA/7snyuoqW8+uH5EcTYzJxZzUdlQ8jNTenQSxvSWJShjekhEyoG9wH3AraraVvR4T0Sm9+ajQ2xr35tpCTBcVfeLyOeBfwBjDnuT6jxgHkBZWVnYHlFvf+809tY2snVvPe9v3sMrH2/nzhdW8X+vrOGSqcP4+uljyMtI7vkZGdMDlqCM6bkvq+r6UC+o6hd78bkVwNCg9SE4paTgz68Oev6ciPxBRApUdWdPDpiTlkROWhLD8zM4YVQ+N5wymrVVNcx7az1/WrCJJ8or+O7Z4/mPqcNISOh1M5sxXWJtUMb0ULjkFAGLgDEiMkJEknE6Y8wP3kFEBrV1yBCRqTi/5V2RDGJ0URZ3XjCRF285mWOG5vDjfyzjknsXsHVvXSQPY0xYlqCM8RlVbQZuAl4EVgCPqepyEbleRK53d7sAWOa2Qf0GuFijdFPj6KIs/nzNNO780jEs27KPGb9+i1dXbI/GoYw5RExv1C0rK1O7D8P4jYiUq2qZ13FEWyR+f5t2HeDGvyxh2ZZqvnHGWL5++mgi0LPe9HPhfoPWBmVML4jIiUApQb8lVX3Ys4CibHh+Bo9ffyI/eOojfvXKatbt2M+dFxxDalLA69BMH2QJypgeEpE/AaOAD4AWd7MCfTZBAaQmBfjllycyuiiTO19YxfbqeuZdXkZOWpLXoZk+ptMEJSJDcX5wg4BWYJ6q/p+IzAGuBXa4u/5AVZ+LVqDG+FAZMCFabT9+JiLccMpoSgak8e2/L+Wiue/yp2umUZhl90yZyOlKJ4lm4FuqegRwPHBj0LArvwoaasWSk+lvluFcuPVbs44t4b4rjmPTrloumvsulfush5+JnE4TlKpWquoS93kNTq+ikmgH1p+t37GfX7y40rrz+l8B8LGIvCgi89sWr4OKtc+MLeTha6ayo6aBi+dZN3QTOd3qZi4ipcAk4D13000i8qGI3C8iuWHeM1tEFovI4h07doTapd/prNfT5j11/P71dVTuqw+7z5w5c6Ieh+nUHOA84OfAL4OWfue40jwevmYqu/c3ctE8K0mZyOhyghKRTJyxxm5x72K/G6eB+FigkjA/TFWdp6plqlpWWNjrKXf6hUT3Tv2W1vBNG+Xl5bEKx4Shqm8CK4Esd1nhbuuXJg3L5U9fncbeA01cMm8B26vDX2AZ0xVdSlAikoQ7EKaqPgmgqttVtUVVW4F7cUZgNhEQcBNUc0tr2H2eeeaZWIVjwhCRC4GFwJeBC3HG4LvA26i8dezQATx4tVPd95U/vmcjo5te6TRBucOp3IdzdXhX0PbioN3Ox2kwNhFwsATVQeewmTNnxiocE94PgeNU9QpVvRznIu3HHsfkuSnDc7nvyuP4ZHctl9+/kOr6Jq9DMnGqKyWo6cBlwGki8oG7fB64U0Q+EpEPgVOBb0Qz0P7k0xJU+AT17LPPxiocE16CqlYFre/Chg8D4PiR+cy9bAqrt9dwzYOLqGts6fxNxrTT6X1Qqvo2oYf/t27lUZKY4PyN66gNyvjCCyLyIvBXd/0i7Hdx0CnjivjVRcfyn399nxseKWfe5WUkBSx/m66zb4sPHSxBtYZvgzLeU9Xv4My1dAwwEecm9u95G5W/nHPMYH5+/tG8vmoH3338Q1rtost0gw115EOJASdBNXVQxdcPBy/wJVV9AqcDkQnjkqnD2H2gkV+8uIr8jGR++IUj7BYH0yVWgvKhtk4SrR0koXnz5sUqHNOOiLztPtaISHXQUiMi1Z29vz+64ZRRXHliKX98ewNz34rWNFqmr7EE5UNtbVAdlaCuu+66WIVj2lHVk9zHLFXNDlqyVDXb6/j8SET4yTkTOOeYYu54fiVPLqnwOiQTByxB+VBbFV9H90EZ77mjmXe6zTgSEoRfXjiR6aPz+e7jH/LGqqrO32T6NUtQPnSwDcoalP3uyOAVEUkEpngUS1xISQxwz1emMHZgFjc8soQPK/Z6HZLxMUtQPnSwm3kHJaj58/vdmKS+ISLfF5Ea4Jjg9idgO/C0x+H5XlZqEg9edRx5Gclc9cAiNu064HVIxqcsQfnQwSq+DkpQU6bYhbpXVPV/VDUL+EW79qd8Vf2+1/HFg6LsVB66eiotqlx+/0J22pBIJgRLUD6U1IVOEiUlNuOJV0RkvPv07yIyuf3iaXBxZFRhJvddcRzbq+u5+sFFHGho9jok4zOWoHzIOkn43jfdx1+GWP7Xq6Di0ZThufz2ksks27KPGx5ZQpN9500QS1A+1HYflHWS8CdVne0+nhpiOc3r+OLNmRMG8t/nH82bq3dw6xMf2U3o5iBLUD4kIiQmSIdXk9dee20MIzKhiMiXRSTLff4jEXlSRCZ5HVc8umTqMG45YwxPLKngFy+u8joc4xOWoHwqKZDQYRWfjSThCz9W1RoROQn4HPAQcI/HMcWtm08fwyVTh/GHN9bxwDsbvA7H+IAlKJ9KCkiHnSSsF58vtM0h8QXgblV9Gkj2MJ64JiL87LyjOGvCQP7r2Y95ZulWr0MyHrME5VPJiQkdVvEtWbIkhtGYMLaIyFyc2XSfE5EU7DfVK4EE4TeXTOK44Xl887EPeHvNTq9DMh6yH5NPJSZ0nKCML1wIvAjMUNW9QB7wHW9Din+pSQHuvaKMUYWZzP7TYj7YbKNN9FeWoHwqKVE6nFG3uLg4htGYUFS1FlgHfE5EbgKKVPUlj8PqE3LSknj46qnkZyZz1QMLWVtV43VIxgOWoHwqKZBAQwclqK1brX7eayJyM/AIUOQufxaR//Q2qr6jKDuVP109jUBCApfdt5CKPbVeh2RizBKUTyV30otvzpw5sQvGhHMNME1Vf6KqPwGOB6z/fwSVFmTw8NVT2d/QzGX3LWRHjQ2J1J9YgvKppEACjc3hE9Ttt98ew2hMGMKnPflwn9tUsRE2YXA2D1x5HNv21XP5/QvZV9vkdUgmRixB+ZTTi8/uqPe5B4D3RGSOiNwOLADu8zimPqmsNI95l09hXdV+rnxwIftt3L5+wRKUTyUFpMMSlPGeqt4FXAXsBnYBV6nqr72Nqu86eUwhv7t0Eh9W7OOrDy2irrGl8zeZuGYJyqeSEwM0dtAGtXjx4hhGYzohgGLVe1F31pGDuOvCiby3YTez/7SY+iZLUn2ZJSifSrYSlO+JyE9whjfKBQqAB0TkR95G1ffNOraE//elY/jXmp3c8MgSGpotSfVVlqB8KjkxocMSVFlZWQyjMWFcAhynqnNU9TacXnz/4XFM/cKFZUP5+flH89rKKm58ZIldzPVRlqB8KjmQYFeG/rcRSA1aT8G5cdfEwKXThvHT847ilRVVVpLqoyxB+VRKYsCuCv2vAVguIg+KyAPAMmC/iPxGRH7Tmw8WkRkiskpE1orIrSFeF/c4a0Xkw/46k+9lxw/np7OO5JUV2/nan5dYm1Qfk+h1ACa05MSO74O67bbbYhiNCeMpd2nzRiQ+VEQCwO+BM4EKYJGIzFfVj4N2OxsY4y7TgLvdx37nshNKERF+9I9lzP5TOfMum0JqUsDrsEwEWILyqc4SlI0k4T1VfShKHz0VWKuq6wFE5FFgFhCcoGYBD6sz/ewCERkgIsWqWhmlmHztK8cPJykg3PrkR1z1wCL+eEUZGSn25y3edVrFJyJDReR1EVkhIsvd8ccQkTwReVlE1riPudEPt/9ISUygoYMENXjw4BhGY2KsBNgctF7hbuvuPojIbBFZLCKLd+zYEfFA/eSi44Zx14UTWbhxN1+57z0bcaIP6EobVDPwLVU9AqeX0o0iMgG4FXhVVccAr7rrJkJSEgM0tyotraFHk6is7JcXyv1FqPup2n8RurIPqjpPVctUtaywsDAiwfnZ+ZOG8PtLJ7Nsyz4uvncBVTX1XodkeqHTBKWqlaq6xH1eA6zAuVKbhXMPCO7jedEKsj9KSXL+a6yjRL9UAQwNWh8CtB++viv79EszjhrE/Vcex6ZdB/jyPe/yyS4bBT1edasXn4iUApOA94CBbfXd7mNRpIPrz1ISnf+acL2SJk/ul522fEFEnhGR+eGWCBxiETBGREaISDJwMdD+c+cDl7u9+Y4H9vXX9qdQTh5TyJ+/Oo19dU188e5/s3zrPq9DMj3Q5QQlIpnAE8Atqlrdjff1mzrwSEpJdHohhWuHKi8vj2U45lD/C/wS2ADUAfe6y36crua9oqrNwE04s/WuAB5T1eUicr2IXO/u9hywHljrHvuG3h63r5k8LJfHrz+BpIBw0dwFNn18HOpSghKRJJzk9IiqPulu3i4ixe7rxUBVqPf2tzrwSOmsBDV79uxYhmOCqOqbqvomMElVL1LVZ9zlUuCkCB3jOVUdq6qjVPW/3W33qOo97nNV1Rvd149WVRucMYTRRVk8ecOJlAxI48oHFvJ4eYXXIZlu6EovPsGZQmCFO3pzm/nAFe7zK4CnIx9e/9V2H0e4EtS9994by3BMaIUiMrJtRURGAHYV5jPFOWn8/WsnMG1kHt/++1Luenk1Tu9843dduVFgOnAZ8JGIfOBu+wFwB/CYiFwDfAJ8OToh9k+dlaCML3wDeENE1rvrpcB13oVjwslOTeKBK6fyw6c+4jevrmHDzgP84oJj7IZen+s0Qanq24SfRuD0yIZj2nRWgjLeU9UXRGQMMN7dtFJVbU5yn0pOTODOC45hRGEGd76wik27DjDvsjIG5aR2/mbjCRuLz6dSkzouQW3ZsiWW4ZgQRCQd+A5wk6ouBYaJyDkeh2U6ICLccMpo5l02hbVV+5n5u7cp37TH67BMGJagfKqtBBUuQVkvPl94AGgETnDXK4CfeReO6aqzjhzEUzdMJy0pwCXzFvDIe5usXcqHLEH5VFuCqguToM4999xYhmNCG6WqdwJNAKpah82qGzfGDcpi/k3TOWFUPj98ahnfefxDm0beZyxB+VRastsG1WRtUD7WKCJpuEMMicgonCk4TJwYkJ7M/Vcex9dPH8MTSyo4/w/vsG7Hfq/DMi5LUD6V6vbiq21s9jgS04E5wAvAUBF5BGdMyu96GpHptkCC8M0zx/LgVVPZXl3PzN++zZNL7H4pP7AE5VPpyU4Hy/owvfjmzp0by3BMCKr6EvBF4Ergr0CZqr7hZUym5z47tpDnbj6Zowbn8M3HlvKNv31ATb2NiO4lS1A+lXKwBGUjSfiViLwKTFPVf6rqs6q6U0TmeR2X6bninDT+cu00vnHGWJ7+YAtn/9+/WLhht9dh9VuWoHwqIUFITUoI24vPGeDDeGwE8D0RCZ7euMyrYExkJAYSuPmMMfz9+hNIEOGiee/yP8+tsJvmPWAJysfSkxOtDcrf9uLcrD7QHeE8x+uATORMGZ7HczefzCVThzH3rfWc89u3WfKJ3TMVS5agfCwtKRC2is/4gqhqs6regDOY8tvYtDN9SmZKIj8//2gevnoqtQ3NfOnuf3P7M8s50GAXjrFgCcrH0pIDYe/LOOccG7DAB+5pe6KqD+J0lnjJq2BM9HxmbCEvfuMzfGXacB54ZyNn/eotXvl4u9dh9XmWoHwsIzkQ9kbdZ555JsbRmDYiku0+/buI5LUtOPNDfdvD0EwUZaUm8dPzjuLx608gIyXAVx9ezFcfWszm3TZjb7RYgvKxtOQAtQ2hE9TMmTNjHI0J8hf3sRxY7D6WB62bPqysNI9/fv1kvn/2eN5Zu5PT73qTu15aZe3FUdCV6TaMR9KTE6mqqQ/52rPPPhvjaEwbVT3HfRzhdSzGG0mBBK777CjOPXYwP39uJb95bS1/W7yZb581ji9OHkIgwXrZRoIlKB9LTw5wIEwJynhHRCZ39LqqLolVLMZbxTlp/PaSSVx54nD+69kVfOfxD7n/nY18b8Y4Pju20G4H6SVLUD6WYd3M/eqXHbymwGmxCsT4w5TheTz1tRN59qNK/vfFVVz5wCKmjsjj22eNY+qIPK/Di1uWoHwsIyUxbAnKpgbwjqqe6nUMxn8SEoRzJw5mxpGDeHTRJ/z2tbVcOPddpo/O5+bTx1qi6gHrJOFjGSkBahubQyajefNsRB0/EJGjRORCEbm8bfE6JuOt5MQELj+hlLe+cyo/+sIRrNpWw4Vz3+XCue/yxqoqu7jsBktQPpaRkkirhp4T6rrrrvMgIhPMHeLot+5yKnAnYBN1GcDphfvVk0fyr++exm0zJ/DJrlqufGARn/+NM1p6Y5iBoM2nLEH5WIY7J9R+u2vdry7AGepom6peBUwEUrwNyfhNWnKAq6aP4K3vnsqdFxxDc0sr33xsKSf9v9f4zatr2FFjU4iFY21QPpaZ6vz37K9vpijL42BMKHWq2ioize7Nu1XASK+DMv6UnJjAhWVD+fKUIby5egf3v7ORu15ezW9fW8PZRxXzH9OGMXVEnvX8C2IJyscy3DmhQnWUmD9/fqzDMYdbLCIDgHtxbtLdDyz0NiTjdyLCKeOKOGVcEet27OfPCzbxeHkF85duZWRhBheWDeWLk0ooyk71OlTPWYLysYMlqBBVfFOmTIl1OKYdd5BYgHtE5AUgW1U/9DImE19GFWZy28wj+e7nxvPPjyp5dOEn3PH8Su58YSWfGVvIeceWcNaRAw9OYNrf9M+zjhNZKUlA6ARVUlJivYF8QESOAUpxf0siMlpVn/Q0KBN30pIDXDBlCBdMGcK6Hft5ckkFTy3Zwi1/+4C0pABnTBjIF44exCnjikhNCngdbsxYgvKxT0tQNu20H4nI/cAxwHKgrUuWApagTI+NKszkO58bz7fOHMeijbuZv3Qrzy/bxjNLt5KWFODU8YWcNWEQp44rIic9yetwo8oSlI9luQmqpt568fnU8ao6wesgTN+UkCBMG5nPtJH53H7ukSxYv5vnl1Xy0sfbee6jbQQShLLhuZw6vohTxhUybmBWn+tgYQnKxzJTwieoa6+9NtbhmMO9KyITVPVjrwMxfVtiIIGTxhRw0pgCfjrrKJZW7OWVFdt5dUUVdzy/kjueX8nA7BROGl3I9NH5nDiqgEE58d/JwhKUj6UmBUgOJFBdf3gVn40k4QsP4SSpbUADIICq6jHehmX6soQEYdKwXCYNy+U7nxvPtn31vLm6irdW7+TVldt5YkkFACMKMpg2Io/jSp1laF5a3JWwLEH5XHZaYsgS1JQpUygvL/cgIhPkfuAy4CM+bYMyJqYG5aRy0XHDuOi4YbS2Kh9XVvPuul28t2EXz31UyaOLNgNQmJXC5GEDmDQsl4lDBnD0kJyDtTR+1Wl0bkPwOUCVqh7lbpsDXAvscHf7gao+F60g+7Os1CSq6w4vQS1ZYjM6+MAnqmo3pBnfSEgQjirJ4aiSHK79zEhaW5VV22tYvGkP5Rt38/7mvby43JmqXsQpZR1dksORg7M5othZCjL9MxhKV9Lng8DvgIfbbf+Vqv5vxCMyh8hODV2CMr6wUkT+AjyDU8UHgHUzN36RkCAHE89lxw8HYPeBRpZW7OXDzftYtnUfCzfs5ukPth58T0FmMuMGZTGmKIsxAzMZXZjJqKJM8jOSY15F2GmCUtW3RKQ0+qGYULLTktgXogRVXFzsQTSmnTScxHRW0DbrZm58LS8jmVPHFXHquKKD23YfaGRlZTUfV1azalsNq7fX8NjizdQ2fjqKTXZqIiMLMynNT6e0IIPh+ekMy0tnaG46hVkpUUlevamAvMmdWmAx8C1V3ROhmEyQ7NQktuytO2z71q1bQ+xtYkVEAsBOVf2O17EY01t5GcmcOLqAE0cXHNzW2qps3VfHmqr9rN9xgA0797Nh5wEWbdzD00u3EjxOQHJiAkMGpFGSm8bgnDQGD0ijOCeVQe4yMDuVnLTu37PV0wR1N/BTnKvFn+LMMHp1qB1FZDYwG2DYsGE9PFz/lZ0Wug1qzpw5zJkzJ/YBGQBUtaWzqd+NiWcJCcKQ3HSG5KZz6rhDX6tvaqFiTx2bd9dSsaeWzXvqqNhTy5a99ayorGLn/kNHaJ9QnM1zN5/c7Rh6lKBUdXvbcxG5F3i2g33nAfMAysrKbGyebspJS6K6zpm0MLgIffvtt1uC8t4HIjIf+DtwoG1jb9qgRCQP+BvO8EkbgQtD1U6IyEagBmgBmlW1rKfHNKa7UpMCjC7KZHRRZsjXG5pbqKpuoHJfPduq60kO9Gxmpx4lKBEpVtVKd/V8YFmPjm46lZOWRGNLK3VNLf12wEgfywN2AacFbettG9StwKuqeoeI3Oqufy/Mvqeq6s5eHMuYqEhJDDA0L52heem9+pyudDP/K3AKUCAiFcBtwCkicizOj3EjYNO7RskAd6ytfXVNlqB8xp2kMNJm4fzewLkR+A3CJyhj+rSu9OK7JMTm+6IQiwmhrWFxb20TxTlpB7cvXrzYq5CMS0SG4Ez3Ph3nYu1t4GZVrejFxw5sq51Q1UoRKQqznwIviYgCc92q9FAxWhuwiVt2Se5zbSWovbU2orkPPQD8Bfiyu/4Vd9uZHb1JRF4BBoV46YfdOPZ0Vd3qJrCXRWSlqr7VfqfgNmAR2SEimzr4zAKgP1UZ9rfzBf+e8/BQGy1B+dyAtGQA9tY2HrK9rKzM5oPyXqGqPhC0/qCI3NLZm1T1jHCvicj2tjZeESnGmUY+1GdsdR+rROQpYCpwWIJq957Cjl4XkcX9qbNFfztfiL9z7lnXChMzuRlOCWqPlaD8aKeIfEVEAu7yFZxOE70xH7jCfX4F8HT7HUQkQ0Sy2p7j3ChsHZVMn2MJyudy050S1J52JSjjC1cDFwLbgErgAsLcD9gNdwBnisganKrCOwBEZLCItI13ORB4W0SWAguBf6rqC708rjG+Y1V8PpeaFCA1KeGwKr7bbrvNo4hMG1X9BDg3wp+5Czg9xPatwOfd5+uBiZE8rqu/zeHS384X4uycLUHFgbz0ZHYdODRB2U263hGRn3TwsqrqT2MWTASF6wnYV/W384X4O2er4osDuRnJh/XiGzx4sEfRGJxRI9ovANdg9ywZEzFWgooDeRmHl6AqKyvD7G2iTVV/2fbc7axwM3AV8CjOuJTGmAiwElQcyMtIZs8B6yThJyKSJyI/Az7EudCbrKrfU9WQ3cL9TERmiMgqEVnrDq/U54jI/SJSJSLLgrblicjLIrLGfcz1MsZIEpGhIvK6iKwQkeUicrO7Pa7O2RJUHMjLSGZ3uwQ1ebINpO0VEfkFsAhnsNajVXVOvE43404b8nvgbGACcImITPA2qqh4EJjRblvbuIdjgFfd9b6iGWcapCOA44Eb3f/XuDpnS1BxoCAzhf0NzdQ3fTp5WHl5uYcR9XvfAgYDPwK2iki1u9SISLXHsXXXVGCtqq5X1UacaspZHscUce4oG7vbbZ6FM94h7uN5MQ0qilS1UlWXuM9rgBVACXF2zpag4kB+hnMvVHApavbs2V6F0++paoKqpqlqlqpmBy1ZqprtdXzdVAJsDlqvcLf1B4eMewiEG/cwrrkzok8C3iPOztkSVBzIz0wBOGQSsHvvvdercEzfEmqebhtDq48QkUzgCeAWVY230r0lqHiQn+mUoHbtt44SJuIqgKFB60OArR7FEmvb3fEO6Wjcw3glIkk4yemRoEk04+qcLUHFgUK3BLWj3TTKxkTAImCMiIwQkWTgYpzxAPuDTsc9jFfiTL99H7BCVe8Keimuztnug4oDBSGq+LZs2eJVOKYPUdVmEbkJeBEIAPer6nKPw4q4MBOv3gE8JiLXAJ/w6bQpfcF04DLgIxH5wN32A+LsnC1BxYG05AAZyQGqqj9NUOXl5TaahIkIVX0OeK7THeNYmIlXIcS4h32Bqr5N6PZFiKNztiq+OFGYlXJICerccyM6RqkxxviOJag4UZiVQlWNtUEZY/oPS1BxoigrlZ2WoIwx/YglqDhRlH1oCWru3LkeRmOMMdFnCSpOFGWlsr+hmQMNzYCNJGGM6fssQcWJoiynq3lbKcq5zcEYY/ouS1BxYmB2KgDbq+s9jsQYY2LDElScGJTjlKAsQRlj+gtLUHGirQS1bZ+ToM455xwvwzHGmKizBBUnslKTyEgOUOkmqGeeecbjiIwxJrosQcWRQTmpB6v4Zs6c6XE0xhgTXTYWXxwpzkljq1uCepXFiUwAAB9tSURBVPbZZz2OxsSbgoICLS0t9ToMYw5TXl6+U1UL22+3BBVHinNSWbNmh9dhmDhVWlrK4sWLvQ7DmMOIyKZQ2zut4hOR+0WkSkSWBW3LE5GXRWSN+5gbyWBNaMUD0qiqaaCppdXrUIwxJuq60gb1IDCj3bZbgVdVdQzwqrtuomxwTiqqTldzVZuV20Tfwg27WVEZdzOFmz6i0wSlqm8Bu9ttngU85D5/CDgvwnGZEIoHpAGwdW898+bN8zga09ctWL+LS+9dwKX3LrD774wnetqLb6CqVgK4j0XhdhSR2SKyWEQW79hh7Se9UTLAuReqcl8d1113ncfRmL6scl8dX/tzOUNy06hrauFbjy2ltdVK7Sa2ot7NXFXnqWqZqpYVFh7WScN0w2C3BFWxp87jSExf9/LH29lT28Tcy8r44Rcm8Pbanby52i4wTWz1NEFtF5FiAPexKnIhmXDSkxPJy0hmy15LUCa6Vm2rITs1kbEDM7mobCgD0pP4xwdbvA7L9DM9TVDzgSvc51cAT0cmHNOZkgFpVOypY/78+V6HYvqw1dtrGDcoCxEhOTGBzx9dzEvLtx+c7sWYWOhKN/O/Au8C40SkQkSuAe4AzhSRNcCZ7rqJgZIBaWzZU8uUKVO8DsX0UarKqm01jB2YdXDbeceWUNfUwssfb/cwMtPfdHqjrqpeEual0yMci+mCIblpvL6qipKSEutqbqJie3UD1fXNjBv0aYIqG55LyYA05i/dynmTSjyMzvQnNhZfnBmal05Ds92oa6Jn1fYagENKUAkJwpkTBvLO2p3UN7V4FZrpZyxBxZkhuWleh2D6uNXbDk9QAJ8dV0hDcysL1u/yIizTD1mCijND89IBOPOLl3ociemrVm2voTArhbyM5EO2nzAyn5TEBN5YZd3NTWxYgoozQ3OdBHXujXO8DcT0Wau31zCuXekJIDUpwPEj8+1+KBMzlqDiTFpygMKsFH721Vleh2L6qK176xmaF7oq+ZRxhWzYeYBNuw7EOCrTH1mCikPD8tLZvmGF12GYPkhV2VvbyID05JCvf3asMxrMv9bsjGVYpp+yBBWHhrvtUMZE2oHGFppbldz0pJCvjyjIoDgnlX+vswRlos8SVBwalp9OIDPPuvuaiNtzoBEgbAlKRJg+uoB/r9tlg8eaqLMEFYeG56cz5MaHqdhT63UoppdEZIaIrBKRtSJy2Lxq4viN+/qHIjLZ3T5URF4XkRUislxEbo5EPPvqmgAYkBa6BAUwfXQ+e2ub+NjmiTJRZgkqDg3Pz2Dv24+waZclqHgmIgHg98DZwATgEhGZ0G63s4Ex7jIbuNvd3gx8S1WPAI4Hbgzx3m7bU+uUoHIzQpegAKaPKgDgnbVWzWeiyxJUHCrNz2DfO39lw07rSRXnpgJrVXW9qjYCj+JMBhpsFvCwOhYAA0SkWFUrVXUJgKrWACuAXo9BtKe28xJUUXYqY4oyedsSlIkyS1BxqK0B20pQca8E2By0XsHhSabTfUSkFJgEvNf+AN2dMHRfbcdtUG2mjy5g0cbdNNqwWyaKLEHFIREBYKPdixLvJMS29j0POtxHRDKBJ4BbVPWwRqHuThh6sAQVphdfmxNH5VPf1Mr7n+zp9DON6SlLUHHq4v/+s1Xxxb8KYGjQ+hBga1f3EZEknOT0iKo+GYmA9tY2kZmSSFKg4z8N00bmkyDwzjobl89EjyWoOFWck8aWvXXW1Ty+LQLGiMgIEUkGLsaZDDTYfOBytzff8cA+Va0Upxh9H7BCVe+KVEDOTbodl54ActKSOLokh3ftfigTRZag4tSvbvoSqrB5t7VDxStVbQZuAl7E6eTwmKouF5HrReR6d7fngPXAWuBe4AZ3+3TgMuA0EfnAXT7f25j2dDFBAZw4uoD3P9lrs+yaqOl0wkLjb+t2HGBMiIE9TXxQ1edwklDwtnuCnitwY4j3vU3o9qle2VvXRG4nHSTaTB9VwN1vrGPhht2cOr4o0qEYYyWoeGftUCaS9tY2ddqDr01ZaS7JiQl2P5SJGktQceq2226jMCuF9Tv2ex2K6UP21jZ2eA9UsNSkAMeV5tr9UCZqLEHFqTlz5jCyIIP1VoIyEdLaquyrawo7UGwo00cXsHJbDVU19VGMzPRXlqDi1ODBgxlZmGklKBMx1fVNtCrkdLGKD+Dk0c69Vf9ea93NTeRZgopTlZWVjCrMYE9tE7vdEaiN6Y297k263SlBTRiczYD0JJsfykSFJag4NqowE8BKUSYiDg4U240SVCBBOHFUPm+v3YHT4dCYyLEEFacmT54clKCsHSqWRCSvC8sAr+Psrr3uVBs53ShBgTPL7vbqBlZvtwslE1l2H1ScKi8vp6VVSU5MYK2VoGJtq7t0dB9SABgWm3AiY28PSlAAn3GngX9zdRXjBtk9eSZyrAQVp2bPnk0gQRhZkMG6KktQMbZCVUeq6ohwCxB3vQb21zsjQmSmdO+6tTgnjXEDs3hzdeejpRvTHZag4tS9994LOO1QVoKKuRMitI+v1Dc5U2ekJQe6/d7PjC1g0YY9NuyRiSir4otzo4oyeX5ZJfVNLaQmdf8Pi+mRG9qmPAlFVe9S1bi7MajOHXg4NbH7162fHVvEvf/awLvrdnHGhIGRDs30U1aCinOjCjNoVZsbKsay3KUM+BrOBIIlwPU4U7fHpfqmFhIThMROptoI5bgRuaQnB3h9VVUUIjP9Va9KUCKyEagBWoBmVS2LRFCmc1u2bAFgdJHTk29d1QHGD8r2MqR+Q1VvBxCRl4DJ7pTriMgc4O8ehtYr9U2tpPWwFJ6SGODkMQW8trIKVaWjEqYxXRWJEtSpqnqsJafYKi8vB5w2KBFYax0lvDAMCL5LuhEo9SaU3qtraiGlF9XEpx8xkMp99XxcedjEvsb0iLVBxalzzz0XVSU1KcCQ3DTrKOGNPwELReQpnGnYzwce9jaknmtoaiEtuefXrKeOc6bceG1FFUcOzolUWKYf620JSoGXRKRcRGaH2kFEZovIYhFZvGOHdUONhlGFmVaC8oCq/jdwFbAH2Atcpao/9zaqnqtraiE1seclqMKsFCYOHcArK60dykRGbxPUdFWdDJwN3Cgin2m/g6rOU9UyVS0rLCzs5eFMKKPdQWNbWm2oGQ9sAN4F3geyQv0G4kUkeoKeeUQRSzfvZdu+uOvEaHyoVwlKVbe6j1XAU8DUSARlOjd37tyDz0cXZdLQ3MqWPXUeRtT/iMhXgbdwpmy/3X2c42VMvdGbThJtZhw1CICXP94WiZBMP9fjBCUiGSKS1fYcOAtYFqnATMdmz/60RrWtJ9/aHTVehdNf3QwcB2xS1VOBSUDc1mM7nSR6V6kyuiiLUYUZvLDcEpTpvd58GwcCb4vIUmAh8E9VfSEyYZnOBHfjDe5qbmKqvu2GXBFJUdWVwLjufICIzBCRVSKyVkRuDfG6iMhv3Nc/FJHJQa/dLyJVIhKRC8P6ppZel6DAKUUtWL+bPTYNjOmlHicoVV2vqhPd5Ui3wdh4YEB6MgWZydZRIvYq3FHL/wG8LCJP4wwi2yUiEgB+j9OGOwG4RETa3+h7NjDGXWYDdwe99iAwo8fRtxOp0UhmHFlMS6vy8sfbIxCV6c9sJIk+YmRhJuusq3nMiFOE/bqq7lXVOcCPgfuA87rxMVOBte7FXiPwKDCr3T6zgIfVsQAYICLFAKr6FrC7l6dyUH1TK6m9rOIDOKokm6F5aTz7UWUEojL9mSWoOHXOOeccsm6DxsaWOrPz/SNo/U1Vne8mmq4qATYHrVe427q7T1jduc2jvjkyVXwiwsxjBvPO2p3s2t/Q688z/ZclqDj1zDPPHLI+qjCDvTb9e6wtEJHjevH+UOMBtb9XoCv7hNWd2zzqGiM34PDMiYNpaVWeW2adJUzPWYKKUzNnzjxkfVRbTz5rh4qlU4F3RWSd24HhIxH5sBvvrwCGBq0P4fA2rK7s02utrUpDc2vEEtT4QVmMKcrkmQ8iHqrpRyxBxalnn332kPVRBW3Tv1uCiqGzgVHAacBM4Bz3sasWAWNEZISIJAMXA/Pb7TMfuNztzXc8sE9VI96409DszAUVqQQlIpw7cTALN+6mYk9tRD7T9D+WoPqIktw0khMTWL/TuprHiqpuCrV04/3NwE04N/iuAB5T1eUicr2IXO/u9hywHlgL3Avc0PZ+EfkrzigW40SkQkSu6em51LfNBRWBThJtzp/sNJU9uWRLxD7T9C82WGwfEUgQSvPTWb/DElS0icgSd4ivXu0DoKrP4SSh4G33BD1X4MYw772kaxF3rr7ZSVCR6CTRZkhuOieOyufx8gr+87TRNgWH6TZLUHHK+bt1qBEFGayxNqhYOKKTtiYB4mo477rGthJUZGdlvmDKEL752FIWbdzD1BF5Ef1s0/dZFV+cmjdv3mHbRhRksnl3Lc0trR5E1K+Mx2lrCrecA5zoWXQ9UN8U2TaoNjOOGkRmSiKPLvokop9r+gdLUHHquuuuO2zbiIJ0mlqUrXttJOloCtf21G6p8DrO7qiLQhsUQHpyIudNGsyzH1ayt9ZugTDdYwmqDynNzwBg025rhzLd09AUnSo+gP+YNpzG5lYeL4+rnG18wBJUHzLcTVAbrSef6aa2ElQkO0m0OaI4mynDc/nLe5/QanOWmW6wBBWn5s9vf7sMFGWlkJKYwCe77b6TaBKRq0UkxX0+S0SuE5G4anNqL1ptUG0uO34463ce4M01cTsbifGAJag4NWXKlMO2JSQIw/LSLUFF382q2iAic4BvAiOA20Tk3yIyyNvQeqY+iiUogM8fXczA7BTuf3tDVD7f9E2WoOJUSUno8UKH5qWzebfNrBtlba39nwdOU9VbVfVzwH8Df/AurJ6LVieJNsmJCVx+Qin/WrOTlduqo3IM0/dYgupjhuSmsdmGlom2zSLyIFAEpLVtVNV/4pSm4k5bCSolSiUogP+YNoy0pADz3lwftWOYvsUSVB9TMiCNmvpm9tU1eR1KX3Yl8CbOXE1PiMg3ROQsEfken5au4kq0q/jAmVjz0mnDeHrpVj7ZZRdRpnOWoOLUtddeG3J7Sa5zQb91r1XzRYuqVqvqA6q6FPgyzogsVwLDgIu8jK2n6ptaSRBICkR3OKLZnxlJQIS731wb1eOYvsESVJwKNZIEQHGOk6Aq91mCigU3Wf1CVS9V1RtVdaPXMfVE23Tv0R4vb2B2KhceN4THyyvYbJ15TCcsQcWpUL34AIpzUgGo3GejSZiuq2uKzGy6XXHjqc7Asb9+ZU1MjmfilyWoOLVkyZKQ2wuzUhCBqmqbatt0XX1T5CYr7ExxThpXnljKk+9XsGpbTUyOaeKTJag+JimQQF56MlU1lqBM1zlVfLH7c/C1z44iMyWRO55fEbNjmvhjCSpOFRcXh32tMCuFHZagTDe0tUHFSm5GMjefPobXV+3gtZXbY3ZcE18sQcWprVu3hn0tPzOZ3QcsQZmuq2+ObYICuPyEUkYWZvDTZ1fQ4E6YaEwwS1Bxas6cOWFfy01PZveBuLwdx3ikrjF2nSTaJCcmMGfmkWzYeYDfv74upsc28cESVJy6/fbbw742ID3JbtSNEyIyQ0RWichaEbk1xOsiIr9xX/9QRCZ39b3d4XSSiP2fg8+MLeT8SSXc/cZa6zBhDmMJqg/KSUuiur455LTwxj9EJAD8HjgbmABcIiIT2u12NjDGXWYDd3fjvV0W6zaoYD8+ZwJZqUl86+8f0Nhss0GbT1mC6oMyU5JoadWDUygY35oKrFXV9araCDyKM3xSsFnAw+pYAAwQkeIuvrfLvExQeRnJ/Pz8o1m2pZpfv7LakxiMP1mCilOLFy8O+1pGivOHZn9Dc6zCMT1TAmwOWq9wt3Vln668t8vqm72p4msz46hBXHzcUO5+cx3/sjmjjKtX38hI1oGbyGm7EraeUb4Xalyh9vWy4fbpynsRkdkislhEFu/YEf4P/61nj+fciT3ObxHxk5kTGFuUxdf/+j4VNiK/oRcJKtJ14KZ7ysrKwr6Wkuj8tzZYfb7fVQBDg9aHAO3vHwi3T1fei6rOU9UyVS0rLCwMG8iFZUOZOiKve9FHWHpyIvdcNoXmFuXah8utBsCQ2Iv3HqwDBxCRtjrwjyMRmOm5QIJzcd3Sap0kfG4RMEZERgBbgIuBS9vtMx+4yf19TQP2qWqliOzownvjzoiCDH576SSueWgxNz6yhD9eUUZSwFoi/Kq+qYWd+xuoqmlgZ00DO/Y3sGt/I7v2N7DzQCO79zey+0Ajw/PTmXd5+IvqcHqToELVgU/rxeeZCAmIJah4oKrNInIT8CIQAO5X1eUicr37+j3Aczgz964FaoGrOnqvB6cRcaeMK+Jn5x3F95/8iG8+tpRfX3TswYsuExuqyt7aJrbsrWPbvnoqq+vZtq+ObfsaqKqpZ3t1PdurG8LezpKdmkh+Zgp5GckMy09n/KCsHsXRmwTV5TpwnO6xDBs2rBeHM8Fuu+22sK8dUZzNT86ZQFFWSgwjMj2hqs/hJKHgbfcEPVfgxq6+t6+4ZOow9tU1ccfzK0lMEH5xwTEkWkkqYlSV3Qca+WR3LZ/srqViT5271LJlbx2Ve+upazq0DTuQIBRlpVCUncqIggyOH5nvrGelUpCVTGFmKoVZKeRmJJGSGJkeob1JUF2uAwfmAZSVldklPUTk/qSORpIoLcjg6pM6n3nc7pMyfnb9Z0fR3NLK/760mpr6Zn536STPusLHI1WlqqaB9TsOsHHXATbudB437apl8+5aDjQemoDyMpIZkpvGuIFZnDK2iJLcNAbnpFI8II3inFQKMlNiXpLtTYLqSv25Mcb02E2njSE7LYnb5i/nwrnvMu+yMga5c54ZR31TCxt2HmDdjv2sq3Ie1+/cz4YdBw5JQsmBBIbmpTE83yn9DM9PZ1heOkNy0xmSm0ZGSm/SQXT0OKK+XAdujPGPy08oZVB2Krf87QPO+e3b/OqiiZw8JnyPxL6qobmFdVUHWFNVw6ptNayp2s/aqv1s2nWAtuZmESgZkMaowkzKhucxsjCDkQWZlBakU5yTFndteb1KmX25DtwY4x9nHTmIf9w4nRsfWcJl9y3kyhNL+c7nxvnyqr+3WluVij11rNxWzcptTjJaua2ajbtqD3Z8SkwQSgsyGD8oi5kTBzO6KJPRhZmMLMzoU9Wgfe9/1xjTJ40dmMX8m07ijudX8NC7G3lp+Ta+d/Z4zp04GJH4Khm0qalvYtW2GlZsq2FFZTUrK6tZta3mkKq5YXnpjBuUxeePLmbMwCzGDcxiREEGyYl9v9OIJShjTNxISw5w+6yjOPfYwdw2fzk3P/oB97y5nv88bTSfO3KQb6uwWlqVTbsOHExGKyurWbGtms276w7uk52ayPjibC6YMoRxg7IZX+wko75YSuyq/nvmxpi4NWV4Hk/feBL/eH8Lv31tDTc8soQhuWlcVDaU8yeXMCQ33ZO4VJVt1fWs3r6fNdtrWLmthtXbnaVt8OYEcXraHjNkABeVDWX8oGyOGJzN4JzUuC0JRoslKGNMXAokCF+aMoRZxw7mlRXbefDfG/nly6v55curObokh1PGFXLCqHwmDhkQ8VJIdX0Tn+yqPdh9e/3OA6zbcYB1VfsPGaKpIDOZcYOyuHTqcMYPyuKI4mzGDMzsU+1E0WQJyhgT1xIDCcw4qpgZRxWzeXct//yokpeWb+P3r6/lt6+tJUGcIZTGDsxiWH46g3PSKMhMYUB6EunJAVKTAgQShFZVmpqV+uYW9jc0U1PfzN7aRnbtb2TH/ga276tn6756tuyppbr+0HECB2WnMqoogy9NLnE6LBRlMXZgJvmZdrN8b1iCMsb0GUPz0rn+s6O4/rOjqK5vonzjHt7fvNfpfLC9hldXVNHY0r1BlEUgNz2ZgdmpFOekUjY8l6F5aQzNTWd4fgalBemkJ9uf0miwf1VjTJ+UnZrEqeOLOHV80cFtra3K7tpGdtQ448jVNjbT0NRKiyoBEQIJQlpygPTkAFmpSeSmJ5ObnmTDLHnEEpQxpt9ISBAKMlMosKq3uGCXBcYYY3zJEpQxxhhfkliOaO1Osraplx9TAOyMQDgWQ9+IAXofx3BV7fODu3Xh9+eX/89Y6W/nC/4955C/wZgmqEgQkcWq2v2pGS2GPhmDn+KId/3t37G/nS/E3zlbFZ8xxhhfsgRljDHGl+IxQc3zOgAshjZ+iAH8E0e862//jv3tfCHOzjnu2qCMMcb0D/FYgjLGGNMPWIIyxhjjS3GboETk2yKiIlLg0fF/ISIrReRDEXlKRAbE8NgzRGSViKwVkVtjddyg4w8VkddFZIWILBeRm2MdQ1AsARF5X0Se9SqGeOf19ykWROR+EakSkWVB2/JE5GURWeM+5noZYySF+43G2znHZYISkaHAmcAnHobxMnCUqh4DrAa+H4uDikgA+D1wNjABuEREJsTi2EGagW+p6hHA8cCNHsTQ5mZghUfHjns++T7FwoPAjHbbbgVeVdUxwKvuel8R7jcaV+cclwkK+BXwXcCzHh6q+pKqtk0KswAYEqNDTwXWqup6VW0EHgVmxejYAKhqpaoucZ/X4CSIkljGACAiQ4AvAH+M9bH7EM+/T7Ggqm8Bu9ttngU85D5/CDgvpkFFUQe/0bg657hLUCJyLrBFVZd6HUuQq4HnY3SsEmBz0HoFHiSHNiJSCkwC3vPg8L/GuVDp3gQ/Jpivvk8xNlBVK8H5gw4UdbJ/XGr3G42rc/bldBsi8gowKMRLPwR+AJzldRyq+rS7zw9xitOPxCImQEJs86QkKSKZwBPALapaHeNjnwNUqWq5iJwSy2P3Mb75PpnIa/8bFQn13+1fvkxQqnpGqO0icjQwAljq/kMPAZaIyFRV3RarOILiuQI4BzhdY3dDWQUwNGh9CLA1Rsc+SESScL74j6jqk7E+PjAdOFdEPg+kAtki8mdV/YoHscQzX3yfPLJdRIpVtVJEioEqrwOKpDC/0bg657iq4lPVj1S1SFVLVbUU58c1ORrJqTMiMgP4HnCuqtbG8NCLgDEiMkJEkoGLgfkxPD7iXB3cB6xQ1btieew2qvp9VR3ifg8uBl6z5NQjnn+fPDQfuMJ9fgXwtIexRFQHv9G4Oue4SlA+8zsgC3hZRD4QkXticVC3Y8ZNwIs4DZ+PqeryWBw7yHTgMuA099w/cEsyJs745PsUdSLyV+BdYJyIVIjINcAdwJkisganV/AdXsYYYeF+o3F1zjbUkTHGGF+yEpQxxhhfsgRljDHGlyxBGWOM8SVLUMYYY3zJEpQxxhhfsgRljDHGlyxBGWOiyp0W55dB698WkTkxjmF/0PN/R+Dz5ojIt0NsHyAiN0TyWL0lIkNE5KJ22+aKyHQROUVE/uRVbJ2xBGWMibYG4Is9mbtNHBH9O6WqJ0by89oZABxMUFE+VledDkxut20aziwMxwLvxzyiLrIEZYyJtmZgHvCN9i+IyDdFZJm73OJuK3Un2vsDsAQ42Z0c9I/ufo+IyBki8o478d7UoM/7h4iUu5P0zQ4VTFtpSkSuDxplYYOIvO5u/4qILHS3z3XnzEJEfijOxI6vAOPCnOsdwCj3vb8IOlZpN84h5PGDXp/SFqu7fpSIvBvmXE8C7gIucD9vhIgcAaxW1RZgIlAiIu+JyHrfDbysqrbYYostUVuA/UA2sBHIAb4NzAGmAB8BGUAmsBxnWohSnClUjnffX4qT5I7GuaguB+7HGYl9FvCPoGPluY9pwDIgvy2G4HjaxZcE/AuYCRwBPAMkua/9Abg8KNZ091zWAt8Oca6lwLL2x+rqOYQ7frtjpONMOdS2/iRwRgf//i/gTK7atv5N4Gr3+fvAHPf5WcC/vP6+BC++HM3cGNO3qDPVw8PA14E6d/NJwFOqegBARJ4ETsYZ0HSTqi4I+ogNqvqRu99ynFlhVUQ+wvnj3+brInK++3woMAbY1Ul4/4cz2PAzInITTjJa5M6YkIYz4neeG2utG0NPBtTtyjmcHub4B6lqrYjUi8gAYCSQq6qviEgGTkJrBN5Q1bYpgMYBq4I+4nPAVSKSCOQDP3e3fwB0uxo2mixBGWNi5dc4VXYPuOsdTU50oN16Q9Dz1qD1Vty/Y2711BnACe4f8TdwpmIJS0SuBIbjDJjbFtNDqvr9dvvdQu/nyer0HMIdP4SPgfHAj4Efudu+CDzuJtq/AY+ISD6wT1Wb3PNIBwao6lYROQZnNuVG9/2TAT9NBGttUMaY2FDV3cBjwDXupreA80Qk3b36Px+nqq2ncoA9bnIaDxzf0c4iMgWnuvErqto2K/OrOO01Re4+eSIy3I31fBFJE5EsnOrAUGpwZjnoqXDHb285cBXOgN/vuNuG8OnsyC3u4wgOnd/rVKCt/WoiMEJEUsSZ2PA2nIsI37ASlDEmln6JW1pR1SUi8iCw0H3tj6r6vjhTlPfEC8D1IvIhTpXWgk72vwmn6u51tzptsap+VUR+BLzk9h5sAm5U1QVuqeQDYBNhEqmq7nI7PiwDnu/uCajqx6GO7x4z2HLgIeC4oG0VOEnqAz4tfKwECtx4ZgNnA4+7r03EmQn83zhViT9tV63qOZtuwxhj+gC3FPo7oB54O6gNKnifJcC0tio/v7MEZYwxxpesDcoYY4wvWYIyxhjjS5agjDHG+JIlKGOMMb5kCcoYY4wvWYIyxhjjS5agjDHG+JIlKGOMMb5kCcoYY4wv/X/ZbbdW7aagmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the desired response of the system\n",
    "a = 0.2\n",
    "P = ct.ss2tf(lateral_normalized)\n",
    "Fm = ct.TransferFunction([a**2], [1, 2*a, a**2])\n",
    "Fr = Fm / P\n",
    "\n",
    "# Compute the step response of the feedforward components\n",
    "t, y_ffwd = ct.step_response(Fm, np.linspace(0, 25, 100))\n",
    "t, delta_ffwd = ct.step_response(Fr, np.linspace(0, 25, 100))\n",
    "\n",
    "# Scale and shift to correspond to lane change (-2 to +2)\n",
    "y_ffwd = 0.5 - 1 * y_ffwd\n",
    "delta_ffwd *= 1\n",
    "\n",
    "# Overhead view\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.plot(y_ffwd, t)\n",
    "plt.plot(-1*np.ones(t.shape), t, 'k-', linewidth=1)\n",
    "plt.plot(0*np.ones(t.shape), t, 'k--', linewidth=1)\n",
    "plt.plot(1*np.ones(t.shape), t, 'k-', linewidth=1)\n",
    "plt.axis([-5, 5, -2, 27])\n",
    "\n",
    "# Plot the response\n",
    "plt.subplot(2, 2, 2)\n",
    "plt.plot(t, y_ffwd)\n",
    "# plt.axis([0, 10, -5, 5])\n",
    "plt.ylabel('Normalized position y/b')\n",
    "\n",
    "plt.subplot(2, 2, 4)\n",
    "plt.plot(t, delta_ffwd)\n",
    "# plt.axis([0, 10, -1, 1])\n",
    "plt.ylabel('$\\\\delta$ [rad]')\n",
    "plt.xlabel('Normalized time $v_0 t / b$');\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fundamental Limits (Example 14.13)\n",
    "\n",
    "Consider a controller based on state feedback combined with an observer where we want a faster closed loop system and choose $\\omega_\\text{c} = 10$, $\\zeta_\\text{c} = 0.707$, $\\omega_\\text{o} = 20$, and $\\zeta_\\text{o} = 0.707$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [100.   -35.86]\n",
      "L =  [ 28.28 400.  ]\n",
      "C(s) =  \n",
      "-1.152e+04 s + 4e+04\n",
      "--------------------\n",
      "s^2 + 42.42 s + 6658\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Compute the feedback gain using eigenvalue placement\n",
    "wc = 10\n",
    "zc = 0.707\n",
    "eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "K = ct.place(A, B, eigs)\n",
    "kr = np.real(1/clsys(0))\n",
    "print(\"K = \", np.squeeze(K))\n",
    "\n",
    "# Compute the estimator gain using eigenvalue placement\n",
    "wo = 20\n",
    "zo = 0.707\n",
    "eigs = np.roots([1, 2*zo*wo, wo**2])\n",
    "L = np.transpose(\n",
    "    ct.place(np.transpose(A), np.transpose(C), eigs))\n",
    "print(\"L = \", np.squeeze(L))\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "C1 = ct.ss2tf(ct.StateSpace(A - B@K - L@C, L, K, 0))\n",
    "print(\"C(s) = \", C1)\n",
    "\n",
    "# Compute the loop transfer function and plot Nyquist, Bode\n",
    "L1 = P * C1\n",
    "plt.figure(); ct.nyquist_plot(L1, np.logspace(0.5, 3, 500))\n",
    "plt.figure(); ct.bode_plot(L1, np.logspace(-1, 3, 500));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K =  [100.   2.]\n",
      "C(s) =  \n",
      "    3628 s + 4e+04\n",
      "---------------------\n",
      "s^2 + 80.28 s + 156.6\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Modified control law\n",
    "wc = 10\n",
    "zc = 2.6\n",
    "eigs = np.roots([1, 2*zc*wc, wc**2])\n",
    "K = ct.place(A, B, eigs)\n",
    "kr = np.real(1/clsys(0))\n",
    "print(\"K = \", np.squeeze(K))\n",
    "\n",
    "# Construct an output-based controller for the system\n",
    "C2 = ct.ss2tf(ct.StateSpace(A - B@K - L@C, L, K, 0))\n",
    "print(\"C(s) = \", C2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the gang of four for the two designs\n",
    "ct.gangof4(P, C1, np.logspace(-1, 3, 100))\n",
    "ct.gangof4(P, C2, np.logspace(-1, 3, 100))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
